Qin, Fan An analog of Leclerc’s conjecture for bases of quantum cluster algebras. (English) Zbl 07292469 SIGMA, Symmetry Integrability Geom. Methods Appl. 16, Paper 122, 22 p. (2020). MSC: 13F60 PDF BibTeX XML Cite \textit{F. Qin}, SIGMA, Symmetry Integrability Geom. Methods Appl. 16, Paper 122, 22 p. (2020; Zbl 07292469) Full Text: DOI
Mcglade, Finn; Ram, Arun; Yang, Yaping Positive level, negative level and level zero. (English) Zbl 07273423 Hu, Jianxun (ed.) et al., Schubert calculus and its applications in combinatorics and representation theory. Selected papers presented at the “International Festival in Schubert Calculus”, Guangzhou, China, November 6–10, 2017. Singapore: Springer (ISBN 978-981-15-7450-4/hbk; 978-981-15-7451-1/ebook). Springer Proceedings in Mathematics & Statistics 332, 153-194 (2020). MSC: 17B37 17B67 PDF BibTeX XML Cite \textit{F. Mcglade} et al., in: Schubert calculus and its applications in combinatorics and representation theory. Selected papers presented at the ``International Festival in Schubert Calculus'', Guangzhou, China, November 6--10, 2017. Singapore: Springer. 153--194 (2020; Zbl 07273423) Full Text: DOI
Gunawan, Emily; Scrimshaw, Travis Kirillov-Reshetikhin crystals \(B^{1, s}\) for \(\widehat{\mathfrak{s}\mathfrak{l}}_n\) using Nakajima monomials. (English) Zbl 1452.17018 Algebr. Represent. Theory 23, No. 4, 1-27 (2020). Reviewer: Daniel Orr (Blacksburg) MSC: 17B37 05E10 PDF BibTeX XML Cite \textit{E. Gunawan} and \textit{T. Scrimshaw}, Algebr. Represent. Theory 23, No. 4, 1--27 (2020; Zbl 1452.17018) Full Text: DOI
Kimura, Yoshiyuki Introduction to quiver varieties. (English) Zbl 07215983 Iohara, Kenji (ed.) et al., Two algebraic byways from differential equations: Gröbner bases and quivers. Cham: Springer (ISBN 978-3-030-26453-6/hbk; 978-3-030-26454-3/ebook). Algorithms and Computation in Mathematics 28, 231-270 (2020). Reviewer: Piotr Malicki (Toruń) MSC: 16G20 16R10 PDF BibTeX XML Cite \textit{Y. Kimura}, Algorithms Comput. Math. 28, 231--270 (2020; Zbl 07215983) Full Text: DOI
Schiffmann, Olivier; Vasserot, Eric On cohomological Hall algebras of quivers: generators. (English) Zbl 1452.16017 J. Reine Angew. Math. 760, 59-132 (2020). Reviewer: Tolulope Oke (College Station) MSC: 16G20 14D23 PDF BibTeX XML Cite \textit{O. Schiffmann} and \textit{E. Vasserot}, J. Reine Angew. Math. 760, 59--132 (2020; Zbl 1452.16017) Full Text: DOI
Bittmann, Léa Asymptotics of standard modules of quantum affine algebras. (English) Zbl 07144052 Algebr. Represent. Theory 22, No. 5, 1209-1237 (2019). MSC: 17B37 17B10 16T20 PDF BibTeX XML Cite \textit{L. Bittmann}, Algebr. Represent. Theory 22, No. 5, 1209--1237 (2019; Zbl 07144052) Full Text: DOI arXiv
Lubovsky, Arthur; Scrimshaw, Travis Alcove path model for \(B(\infty)\). (English) Zbl 1426.05177 J. Pure Appl. Algebra 223, No. 11, 4778-4800 (2019). Reviewer: Matthew Fayers (London) MSC: 05E10 17B37 05C78 05C20 17B67 PDF BibTeX XML Cite \textit{A. Lubovsky} and \textit{T. Scrimshaw}, J. Pure Appl. Algebra 223, No. 11, 4778--4800 (2019; Zbl 1426.05177) Full Text: DOI
Oh, Se-jin; Scrimshaw, Travis Categorical relations between Langlands dual quantum affine algebras: exceptional cases. (English) Zbl 1439.81063 Commun. Math. Phys. 368, No. 1, 295-367 (2019); correction ibid. 371, No. 2, 833-837 (2019). Reviewer: Daniel Bulacu (Bucharest) MSC: 81R50 17B81 20C08 16G20 PDF BibTeX XML Cite \textit{S.-j. Oh} and \textit{T. Scrimshaw}, Commun. Math. Phys. 368, No. 1, 295--367 (2019; Zbl 1439.81063) Full Text: DOI
Hernandez, David; Oya, Hironori Quantum Grothendieck ring isomorphisms, cluster algebras and Kazhdan-Lusztig algorithm. (English) Zbl 1448.17019 Adv. Math. 347, 192-272 (2019). MSC: 17B37 17B67 17B10 13F60 PDF BibTeX XML Cite \textit{D. Hernandez} and \textit{H. Oya}, Adv. Math. 347, 192--272 (2019; Zbl 1448.17019) Full Text: DOI
Kashiwara, Masaki; Kim, Myungho; Oh, Se-jin Monoidal categories of modules over quantum affine algebras of type \(A\) and \(B\). (English) Zbl 07015002 Proc. Lond. Math. Soc. (3) 118, No. 1, 43-77 (2019). MSC: 17B37 16T25 18M05 PDF BibTeX XML Cite \textit{M. Kashiwara} et al., Proc. Lond. Math. Soc. (3) 118, No. 1, 43--77 (2019; Zbl 07015002) Full Text: DOI arXiv
Salisbury, Ben; Scrimshaw, Travis Virtual crystals and Nakajima monomials. (English) Zbl 1400.05270 SIGMA, Symmetry Integrability Geom. Methods Appl. 14, Paper 103, 19 p. (2018). MSC: 05E10 17B37 PDF BibTeX XML Cite \textit{B. Salisbury} and \textit{T. Scrimshaw}, SIGMA, Symmetry Integrability Geom. Methods Appl. 14, Paper 103, 19 p. (2018; Zbl 1400.05270) Full Text: DOI arXiv
Kimura, Taro; Pestun, Vasily Quiver W-algebras. (English) Zbl 1388.81850 Lett. Math. Phys. 108, No. 6, 1351-1381 (2018). MSC: 81T60 81R10 14D21 81R50 16G20 PDF BibTeX XML Cite \textit{T. Kimura} and \textit{V. Pestun}, Lett. Math. Phys. 108, No. 6, 1351--1381 (2018; Zbl 1388.81850) Full Text: DOI
Nekrasov, Nikita; Pestun, Vasily; Shatashvili, Samson Quantum geometry and quiver gauge theories. (English) Zbl 1393.81033 Commun. Math. Phys. 357, No. 2, 519-567 (2018). Reviewer: Gabor Etesi (Budapest) MSC: 81T60 81T13 16G20 83E15 81R10 PDF BibTeX XML Cite \textit{N. Nekrasov} et al., Commun. Math. Phys. 357, No. 2, 519--567 (2018; Zbl 1393.81033) Full Text: DOI arXiv
Kang, Seok-Jin; Kashiwara, Masaki; Kim, Myungho Symmetric quiver Hecke algebras and R-matrices of quantum affine algebras. (English) Zbl 1407.81108 Invent. Math. 211, No. 2, 591-685 (2018); correction ibid. 216, No. 2, 597-599 (2019). Reviewer: Uwe Franz (Besançon) MSC: 81R50 16G20 16T25 17B37 PDF BibTeX XML Cite \textit{S.-J. Kang} et al., Invent. Math. 211, No. 2, 591--685 (2018; Zbl 1407.81108) Full Text: DOI
Gunawan, Emily; Scrimshaw, Travis Realization of Kirillov-Reshetikhin crystals \(B^{1,s}\) for \(\widehat{\mathfrak{sl}}_n\) using Nakajima monomials. (English) Zbl 1390.17024 Sémin. Lothar. Comb. 78B, 78B.47, 12 p. (2017). MSC: 17B37 05E10 PDF BibTeX XML Cite \textit{E. Gunawan} and \textit{T. Scrimshaw}, Sémin. Lothar. Comb. 78B, 78B.47, 12 p. (2017; Zbl 1390.17024) Full Text: Link
Awata, Hidetoshi; Kanno, Hiroaki; Matsumoto, Takuya; Mironov, Andrei; Morozov, Alexei; Morozov, Andrey; Ohkubo, Yusuke; Zenkevich, Yegor Explicit examples of DIM constraints for network matrix models. (English) Zbl 1390.81206 J. High Energy Phys. 2016, No. 7, Paper No. 103, 67 p. (2016). MSC: 81R10 PDF BibTeX XML Cite \textit{H. Awata} et al., J. High Energy Phys. 2016, No. 7, Paper No. 103, 67 p. (2016; Zbl 1390.81206) Full Text: DOI
Nekrasov, Nikita BPS/CFT correspondence: non-perturbative Dyson-Schwinger equations and \(qq\)-characters. (English) Zbl 1388.81872 J. High Energy Phys. 2016, No. 3, Paper No. 181, 70 p. (2016). MSC: 81T60 PDF BibTeX XML Cite \textit{N. Nekrasov}, J. High Energy Phys. 2016, No. 3, Paper No. 181, 70 p. (2016; Zbl 1388.81872) Full Text: DOI arXiv
Qin, Fan Quantum groups via cyclic quiver varieties. I. (English) Zbl 1377.16009 Compos. Math. 152, No. 2, 299-326 (2016). Reviewer: Volodymyr Mazorchuk (Uppsala) MSC: 16G20 17B37 PDF BibTeX XML Cite \textit{F. Qin}, Compos. Math. 152, No. 2, 299--326 (2016; Zbl 1377.16009) Full Text: DOI arXiv
Young, Charles Quantum loop algebras and \(\ell\)-root operators. (English) Zbl 1359.17038 Transform. Groups 20, No. 4, 1195-1226 (2015). MSC: 17B67 17B10 17B37 PDF BibTeX XML Cite \textit{C. Young}, Transform. Groups 20, No. 4, 1195--1226 (2015; Zbl 1359.17038) Full Text: DOI
Kang, Seok-Jin; Kashiwara, Masaki; Kim, Myungho; Oh, Se-Jin Symmetric quiver Hecke algebras and \(R\)-matrices of quantum affine algebras. III. (English) Zbl 1322.81056 Proc. Lond. Math. Soc. (3) 111, No. 2, 420-444 (2015). MSC: 17B37 20C08 17B67 17B10 PDF BibTeX XML Cite \textit{S.-J. Kang} et al., Proc. Lond. Math. Soc. (3) 111, No. 2, 420--444 (2015; Zbl 1322.81056) Full Text: DOI arXiv
Zegers, R. \(q\), \(t\)-characters and the structure of the \(\ell\)-weight spaces of standard modules over simply laced quantum affine algebras. (English) Zbl 1394.17053 Transform. Groups 20, No. 2, 573-613 (2015). MSC: 17B67 17B10 17B37 PDF BibTeX XML Cite \textit{R. Zegers}, Transform. Groups 20, No. 2, 573--613 (2015; Zbl 1394.17053) Full Text: DOI arXiv
Kang, Seok-Jin; Kashiwara, Masaki; Kim, Myungho Symmetric quiver Hecke algebras and \(R\)-matrices of quantum affine algebras. II. (English) Zbl 1323.81046 Duke Math. J. 164, No. 8, 1549-1602 (2015). Reviewer: Hu Jun (Beijing) MSC: 17B37 20C08 17B67 17B10 PDF BibTeX XML Cite \textit{S.-J. Kang} et al., Duke Math. J. 164, No. 8, 1549--1602 (2015; Zbl 1323.81046) Full Text: DOI Euclid arXiv
Li, Jian-Rong On the extended T-system of type \(C_3\). (English) Zbl 1327.17012 J. Algebr. Comb. 41, No. 2, 577-617 (2015). MSC: 17B37 81R50 82B23 PDF BibTeX XML Cite \textit{J.-R. Li}, J. Algebr. Comb. 41, No. 2, 577--617 (2015; Zbl 1327.17012) Full Text: DOI arXiv
Chari, Vyjayanthi; Venkatesh, R. Demazure modules, fusion products and \(Q\)-systems. (English) Zbl 1361.17024 Commun. Math. Phys. 333, No. 2, 799-830 (2015). MSC: 17B67 17B10 PDF BibTeX XML Cite \textit{V. Chari} and \textit{R. Venkatesh}, Commun. Math. Phys. 333, No. 2, 799--830 (2015; Zbl 1361.17024) Full Text: DOI arXiv
Maksimau, Ruslan Canonical basis, KLR algebras and parity sheaves. (English) Zbl 1387.17030 J. Algebra 422, 563-610 (2015). MSC: 17B37 14L35 14F05 16E20 PDF BibTeX XML Cite \textit{R. Maksimau}, J. Algebra 422, 563--610 (2015; Zbl 1387.17030) Full Text: DOI arXiv
Hiroe, Kazuki; Yamakawa, Daisuke Moduli spaces of meromorphic connections and quiver varieties. (English) Zbl 1298.53090 Adv. Math. 266, 120-151 (2014). MSC: 53D30 16G20 53D20 PDF BibTeX XML Cite \textit{K. Hiroe} and \textit{D. Yamakawa}, Adv. Math. 266, 120--151 (2014; Zbl 1298.53090) Full Text: DOI arXiv
Kimura, Yoshiyuki; Qin, Fan Graded quiver varieties, quantum cluster algebras and dual canonical basis. (English) Zbl 1331.13016 Adv. Math. 262, 261-312 (2014). Reviewer: Robert Marsh (Leeds) MSC: 13F60 16G20 18D10 20G42 PDF BibTeX XML Cite \textit{Y. Kimura} and \textit{F. Qin}, Adv. Math. 262, 261--312 (2014; Zbl 1331.13016) Full Text: DOI arXiv
De Concini, Corrado; Hernandez, David; Reshetikhin, Nicolai Geometry of the analytic loop group. (English) Zbl 1343.17009 Adv. Math. 238, 290-321 (2013). MSC: 17B37 14H52 17B63 22E67 PDF BibTeX XML Cite \textit{C. De Concini} et al., Adv. Math. 238, 290--321 (2013; Zbl 1343.17009) Full Text: DOI arXiv
Leclerc, Bernard; Plamondon, Pierre-Guy Nakajima varieties and repetitive algebras. (English) Zbl 1285.14050 Publ. Res. Inst. Math. Sci. 49, No. 3, 531-561 (2013). Reviewer: Alan Koch (Decatur) MSC: 14L24 16G20 17B37 PDF BibTeX XML Cite \textit{B. Leclerc} and \textit{P.-G. Plamondon}, Publ. Res. Inst. Math. Sci. 49, No. 3, 531--561 (2013; Zbl 1285.14050) Full Text: DOI arXiv
Mukhin, E.; Young, C. A. S. Path description of type B \(q\)-characters. (English) Zbl 1323.17015 Adv. Math. 231, No. 2, 1119-1150 (2012). MSC: 17B37 PDF BibTeX XML Cite \textit{E. Mukhin} and \textit{C. A. S. Young}, Adv. Math. 231, No. 2, 1119--1150 (2012; Zbl 1323.17015) Full Text: DOI arXiv
Frenkel, Edward; Hernandez, David Langlands duality for finite-dimensional representations of quantum affine algebras. (English) Zbl 1222.17014 Lett. Math. Phys. 96, No. 1-3, 217-261 (2011). Reviewer: Sorin Dascalescu (Bucureşti) MSC: 17B37 17B10 81R50 PDF BibTeX XML Cite \textit{E. Frenkel} and \textit{D. Hernandez}, Lett. Math. Phys. 96, No. 1--3, 217--261 (2011; Zbl 1222.17014) Full Text: DOI arXiv
Nakajima, Hiraku Quiver varieties and cluster algebras. (English) Zbl 1223.13013 Kyoto J. Math. 51, No. 1, 71-126 (2011). Reviewer: Sean Lawton (Edinburg) MSC: 13F60 16G20 14D21 17B37 PDF BibTeX XML Cite \textit{H. Nakajima}, Kyoto J. Math. 51, No. 1, 71--126 (2011; Zbl 1223.13013) Full Text: DOI arXiv
Young, C. A. S.; Zegers, R. Dorey’s rule and the \(q\)-characters of simply-laced quantum affine algebras. (English) Zbl 1229.17021 Commun. Math. Phys. 302, No. 3, 789-813 (2011). Reviewer: Gastón Andrés García (Córdoba) MSC: 17B37 81R50 PDF BibTeX XML Cite \textit{C. A. S. Young} and \textit{R. Zegers}, Commun. Math. Phys. 302, No. 3, 789--813 (2011; Zbl 1229.17021) Full Text: DOI arXiv
Hernandez, David; Leclerc, Bernard Cluster algebras and quantum affine algebras. (English) Zbl 1284.17010 Duke Math. J. 154, No. 2, 265-341 (2010). Reviewer: Sorin Dascalescu (Bucureşti) MSC: 17B37 16D90 18D10 13F60 PDF BibTeX XML Cite \textit{D. Hernandez} and \textit{B. Leclerc}, Duke Math. J. 154, No. 2, 265--341 (2010; Zbl 1284.17010) Full Text: DOI arXiv
Hernandez, David Simple tensor products. (English) Zbl 1221.17015 Invent. Math. 181, No. 3, 649-675 (2010). Reviewer: Hu Jun (Beijing) MSC: 17B37 17B10 PDF BibTeX XML Cite \textit{D. Hernandez}, Invent. Math. 181, No. 3, 649--675 (2010; Zbl 1221.17015) Full Text: DOI arXiv
Hausel, Tamás Kac’s conjecture from Nakajima quiver varieties. (English) Zbl 1198.16016 Invent. Math. 181, No. 1, 21-37 (2010). Reviewer: Volodymyr Mazorchuk (Uppsala) MSC: 16G20 17B67 PDF BibTeX XML Cite \textit{T. Hausel}, Invent. Math. 181, No. 1, 21--37 (2010; Zbl 1198.16016) Full Text: DOI arXiv
Inoue, Rei; Iyama, Osamu; Kuniba, Atsuo; Nakanishi, Tomoki; Suzuki, Junji Periodicities of \(T\)-systems and \(Y\)-systems. (English) Zbl 1250.17024 Nagoya Math. J. 197, 59-174 (2010). Reviewer: Nenad Manojlović (Faro) MSC: 17B37 16T20 13F60 81R12 81R50 82B23 PDF BibTeX XML Cite \textit{R. Inoue} et al., Nagoya Math. J. 197, 59--174 (2010; Zbl 1250.17024) Full Text: DOI arXiv
Kim, Jeong-Ah; Shin, Dong-Uy Monomial realization of crystal bases \(B(\infty)\) for the quantum finite algebras. (English) Zbl 1144.17010 Algebr. Represent. Theory 11, No. 1, 93-105 (2008). Reviewer: Li Fang (Hangzhou) MSC: 17B37 81R50 PDF BibTeX XML Cite \textit{J.-A. Kim} and \textit{D.-U. Shin}, Algebr. Represent. Theory 11, No. 1, 93--105 (2008; Zbl 1144.17010) Full Text: DOI
Hernandez, David On minimal affinizations of representations of quantum groups. (English) Zbl 1141.17011 Commun. Math. Phys. 276, No. 1, 221-259 (2007). Reviewer: Tomasz Brzeziński (Swansea) MSC: 17B37 17B10 46L87 PDF BibTeX XML Cite \textit{D. Hernandez}, Commun. Math. Phys. 276, No. 1, 221--259 (2007; Zbl 1141.17011) Full Text: DOI arXiv
Zhang, Honglian; Jing, Naihuan Drinfeld realization of twisted quantum affine algebras. (English) Zbl 1168.17012 Commun. Algebra 35, No. 11, 3683-3698 (2007). Reviewer: Yang Shilin (Beijing) MSC: 17B37 17B67 PDF BibTeX XML Cite \textit{H. Zhang} and \textit{N. Jing}, Commun. Algebra 35, No. 11, 3683--3698 (2007; Zbl 1168.17012) Full Text: DOI
Hausel, Tamás Betti numbers of holomorphic symplectic quotients via arithmetic Fourier transform. (English) Zbl 1160.53374 Proc. Natl. Acad. Sci. USA 103, No. 16, 6120-6124 (2006). MSC: 53D20 14C05 16G20 PDF BibTeX XML Cite \textit{T. Hausel}, Proc. Natl. Acad. Sci. USA 103, No. 16, 6120--6124 (2006; Zbl 1160.53374) Full Text: DOI arXiv
Hernandez, David; Nakajima, Hiraku Level 0 monomial crystals. (English) Zbl 1201.17008 Nagoya Math. J. 184, 85-153 (2006). Reviewer: Sonia Natale (Córdoba) MSC: 17B37 PDF BibTeX XML Cite \textit{D. Hernandez} and \textit{H. Nakajima}, Nagoya Math. J. 184, 85--153 (2006; Zbl 1201.17008) Full Text: DOI Euclid arXiv
Hernandez, David The Kirillov-Reshetikhin conjecture and solutions of \(T\)-systems. (English) Zbl 1160.17010 J. Reine Angew. Math. 596, 63-87 (2006). MSC: 17B37 17B67 PDF BibTeX XML Cite \textit{D. Hernandez}, J. Reine Angew. Math. 596, 63--87 (2006; Zbl 1160.17010) Full Text: DOI arXiv
Shin, Dong-Uy Crystal bases and monomials for \(U_q(G_2)\)-modules. (English) Zbl 1158.17305 Commun. Algebra 34, No. 1, 129-142 (2006). MSC: 17B37 05E10 81R50 PDF BibTeX XML Cite \textit{D.-U. Shin}, Commun. Algebra 34, No. 1, 129--142 (2006; Zbl 1158.17305) Full Text: DOI arXiv
Hernandez, David Monomials of \(q\) and \(q,t\)-characters for non simply-laced quantum affinizations. (English) Zbl 1098.17010 Math. Z. 250, No. 2, 443-473 (2005). Reviewer: Stefano Capparelli (Roma) MSC: 17B37 17B67 PDF BibTeX XML Cite \textit{D. Hernandez}, Math. Z. 250, No. 2, 443--473 (2005; Zbl 1098.17010) Full Text: DOI arXiv
Hernandez, David The \(t\)-analogs of \(q\)-characters at roots of unity for quantum affine algebras and beyond. (English) Zbl 1127.17015 J. Algebra 279, No. 2, 514-557 (2004). MSC: 17B37 PDF BibTeX XML Cite \textit{D. Hernandez}, J. Algebra 279, No. 2, 514--557 (2004; Zbl 1127.17015) Full Text: DOI
Hernandez, David Algebraic approach to \(q,t\)-characters. (English) Zbl 1098.17009 Adv. Math. 187, No. 1, 1-52 (2004). MSC: 17B37 17B67 PDF BibTeX XML Cite \textit{D. Hernandez}, Adv. Math. 187, No. 1, 1--52 (2004; Zbl 1098.17009) Full Text: DOI arXiv
Nakajima, Hiraku \(t\)-analogs of \(q\)-characters of Kirillov-Reshetikhin modules of quantum affine algebras. (English) Zbl 1078.17008 Represent. Theory 7, 259-274 (2003). Reviewer: Volodymyr Mazorchuk (Uppsala) MSC: 17B37 81R50 82B23 PDF BibTeX XML Cite \textit{H. Nakajima}, Represent. Theory 7, 259--274 (2003; Zbl 1078.17008) Full Text: DOI arXiv