Xia, Limeng; Zhao, Kaiming Twisted Whittaker modules over \(U_q (\mathfrak{gl}_{n+1})\). (English) Zbl 1525.17014 Sci. China, Math. 66, No. 10, 2191-2202 (2023). Reviewer: Mee Seong Im (Annapolis) MSC: 17B37 PDFBibTeX XMLCite \textit{L. Xia} and \textit{K. Zhao}, Sci. China, Math. 66, No. 10, 2191--2202 (2023; Zbl 1525.17014) Full Text: DOI
Dai, Yanmin Explicit generators of the centre of the quantum group. (English) Zbl 07726246 Commun. Math. Stat. 11, No. 3, 541-562 (2023). MSC: 17B37 20G42 19A22 PDFBibTeX XMLCite \textit{Y. Dai}, Commun. Math. Stat. 11, No. 3, 541--562 (2023; Zbl 07726246) Full Text: DOI arXiv
Kuan, Jeffrey; Zhang, Keke Explicit central elements of \(U_q(\mathfrak{gl}(N+1))\). (English) Zbl 07711516 SIGMA, Symmetry Integrability Geom. Methods Appl. 19, Paper 036, 13 p. (2023). Reviewer: Nenad Manojlović (Faro) MSC: 17B37 16T05 16T20 PDFBibTeX XMLCite \textit{J. Kuan} and \textit{K. Zhang}, SIGMA, Symmetry Integrability Geom. Methods Appl. 19, Paper 036, 13 p. (2023; Zbl 07711516) Full Text: DOI arXiv
Xia, Limeng; Wang, Shengyuan; Xu, Senrong The twisted Whittaker modules over the quantum group of type \(B_2\). (English) Zbl 1512.17027 Commun. Algebra 51, No. 1, 135-149 (2023). Reviewer: Li Luo (Shanghai) MSC: 17B37 PDFBibTeX XMLCite \textit{L. Xia} et al., Commun. Algebra 51, No. 1, 135--149 (2023; Zbl 1512.17027) Full Text: DOI
Jakobsen, Hans Plesner Algebras of variable coefficient quantized differential operators. (English) Zbl 1509.81536 J. Math. Phys. 63, No. 8, Article ID 081704, 34 p. (2022). MSC: 81S10 81R60 81Q15 17B37 81R50 16T20 PDFBibTeX XMLCite \textit{H. P. Jakobsen}, J. Math. Phys. 63, No. 8, Article ID 081704, 34 p. (2022; Zbl 1509.81536) Full Text: DOI arXiv
Luo, Yang; Wang, Yongjie; Ye, Yu On the Harish-Chandra homomorphism for quantum superalgebras. (English) Zbl 1501.17013 Commun. Math. Phys. 393, No. 3, 1483-1527 (2022). Reviewer: Yang Shilin (Beijing) MSC: 17B37 PDFBibTeX XMLCite \textit{Y. Luo} et al., Commun. Math. Phys. 393, No. 3, 1483--1527 (2022; Zbl 1501.17013) Full Text: DOI arXiv
Tanisaki, Toshiyuki Differential operators on quantized flag manifolds at roots of unity. III. (English) Zbl 1483.14086 Adv. Math. 392, Article ID 107990, 51 p. (2021). Reviewer: Mee Seong Im (Annapolis) MSC: 14M15 20G05 17B37 PDFBibTeX XMLCite \textit{T. Tanisaki}, Adv. Math. 392, Article ID 107990, 51 p. (2021; Zbl 1483.14086) Full Text: DOI arXiv
Razumov, Alexander V. Quantum groups and functional relations for arbitrary rank. (English) Zbl 07408756 Nucl. Phys., B 971, Article ID 115517, 51 p. (2021). MSC: 81-XX 83-XX PDFBibTeX XMLCite \textit{A. V. Razumov}, Nucl. Phys., B 971, Article ID 115517, 51 p. (2021; Zbl 07408756) Full Text: DOI arXiv
Razumov, A. V. \( \ell \)-weights and factorization of transfer operators. (English. Russian original) Zbl 1471.81050 Theor. Math. Phys. 208, No. 2, 1116-1143 (2021); translation from Teor. Mat. Fiz. 208, No. 2, 310-341 (2021). MSC: 81R50 81Q80 16T25 55P48 PDFBibTeX XMLCite \textit{A. V. Razumov}, Theor. Math. Phys. 208, No. 2, 1116--1143 (2021; Zbl 1471.81050); translation from Teor. Mat. Fiz. 208, No. 2, 310--341 (2021) Full Text: DOI arXiv
Batra, Punita; Yamane, Hiroyuki Natural elements of center of generalized quantum groups. (English) Zbl 1467.17008 Srivastava, Ashish K. (ed.) et al., Categorical, homological and combinatorial methods in algebra. AMS special session in honor of S. K. Jain’s 80th birthday, Ohio State University, Columbus, Ohio, March 16–18, 2018. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 751, 19-31 (2020). Reviewer: Volodymyr Mazorchuk (Uppsala) MSC: 17B37 17B10 81R50 PDFBibTeX XMLCite \textit{P. Batra} and \textit{H. Yamane}, Contemp. Math. 751, 19--31 (2020; Zbl 1467.17008) Full Text: DOI arXiv
Kolb, Stefan; Yakimov, Milen Symmetric pairs for Nichols algebras of diagonal type via star products. (English) Zbl 1473.17040 Adv. Math. 365, Article ID 107042, 69 p. (2020). Reviewer: Sonia Natale (Córdoba) MSC: 17B37 53C35 16T05 17B67 PDFBibTeX XMLCite \textit{S. Kolb} and \textit{M. Yakimov}, Adv. Math. 365, Article ID 107042, 69 p. (2020; Zbl 1473.17040) Full Text: DOI arXiv
Nirov, Khazret S.; Razumov, Alexander V. Vertex models and spin chains in formulas and pictures. (English) Zbl 1460.17024 SIGMA, Symmetry Integrability Geom. Methods Appl. 15, Paper 068, 67 p. (2019). MSC: 17B37 17B80 16T05 16T25 PDFBibTeX XMLCite \textit{K. S. Nirov} and \textit{A. V. Razumov}, SIGMA, Symmetry Integrability Geom. Methods Appl. 15, Paper 068, 67 p. (2019; Zbl 1460.17024) Full Text: DOI arXiv
Lentner, Simon The unrolled quantum group inside Lusztig’s quantum group of divided powers. (English) Zbl 1447.16029 Lett. Math. Phys. 109, No. 7, 1665-1682 (2019). MSC: 16T05 17B69 PDFBibTeX XMLCite \textit{S. Lentner}, Lett. Math. Phys. 109, No. 7, 1665--1682 (2019; Zbl 1447.16029) Full Text: DOI arXiv
Batra, Punita; Yamane, Hiroyuki Centers of generalized quantum groups. (English) Zbl 1430.17043 J. Pure Appl. Algebra 222, No. 5, 1203-1241 (2018). MSC: 17B37 17B10 PDFBibTeX XMLCite \textit{P. Batra} and \textit{H. Yamane}, J. Pure Appl. Algebra 222, No. 5, 1203--1241 (2018; Zbl 1430.17043) Full Text: DOI arXiv
Nirov, Kh. S.; Razumov, A. V. Quantum groups and functional relations for lower rank. (English) Zbl 1356.81151 J. Geom. Phys. 112, 1-28 (2017). MSC: 81R12 81R50 17B37 22E67 16T25 82B20 PDFBibTeX XMLCite \textit{Kh. S. Nirov} and \textit{A. V. Razumov}, J. Geom. Phys. 112, 1--28 (2017; Zbl 1356.81151) Full Text: DOI arXiv
Saito, Yoshihisa Quantized coordinate rings, PBW-type bases and \(q\)-boson algebras. (English) Zbl 1397.17020 J. Algebra 453, 456-491 (2016). MSC: 17B37 20G42 81R10 81R50 PDFBibTeX XMLCite \textit{Y. Saito}, J. Algebra 453, 456--491 (2016; Zbl 1397.17020) Full Text: DOI arXiv
Tanisaki, Toshiyuki The center of a quantized enveloping algebra at an even root of unity. (English) Zbl 1397.17021 Osaka J. Math. 53, No. 1, 47-81 (2016). MSC: 17B37 PDFBibTeX XMLCite \textit{T. Tanisaki}, Osaka J. Math. 53, No. 1, 47--81 (2016; Zbl 1397.17021) Full Text: arXiv Euclid
Lentner, Simon; Nett, Daniel New \(R\)-matrices for small quantum groups. (English) Zbl 1345.17012 Algebr. Represent. Theory 18, No. 6, 1649-1673 (2015). Reviewer: Dmitry Artamonov (Moskva) MSC: 17B37 18D10 16T25 PDFBibTeX XMLCite \textit{S. Lentner} and \textit{D. Nett}, Algebr. Represent. Theory 18, No. 6, 1649--1673 (2015; Zbl 1345.17012) Full Text: DOI arXiv
Sartori, Antonio The Alexander polynomial as quantum invariant of links. (English) Zbl 1329.57021 Ark. Mat. 53, No. 1, 177-202 (2015). Reviewer: Kazuo Habiro (Kyoto) MSC: 57M27 57M25 17B37 PDFBibTeX XMLCite \textit{A. Sartori}, Ark. Mat. 53, No. 1, 177--202 (2015; Zbl 1329.57021) Full Text: DOI arXiv
Angiono, Iván; Yamane, Hiroyuki The \(R\)-matrix of quantum doubles of Nichols algebras of diagonal type. (English) Zbl 1394.17066 J. Math. Phys. 56, No. 2, 021702, 19 p. (2015). MSC: 17B81 81R10 PDFBibTeX XMLCite \textit{I. Angiono} and \textit{H. Yamane}, J. Math. Phys. 56, No. 2, 021702, 19 p. (2015; Zbl 1394.17066) Full Text: DOI arXiv
Hu, Naihong; Shi, Yuxing On the centre of two-parameter quantum groups \(U_{r, s}(\mathfrak{g})\) for type \(B_n\) with \(n\) even. (English) Zbl 1362.17022 J. Geom. Phys. 86, 422-433 (2014). MSC: 17B37 17B35 PDFBibTeX XMLCite \textit{N. Hu} and \textit{Y. Shi}, J. Geom. Phys. 86, 422--433 (2014; Zbl 1362.17022) Full Text: DOI arXiv
Tanisaki, Toshiyuki Differential operators on quantized flag manifolds at roots of unity. II. (English) Zbl 1311.14047 Nagoya Math. J. 214, 1-52 (2014). Reviewer: Gwyn Bellamy (Glasgow) MSC: 14M15 20G05 17B37 14F10 14A22 32C38 PDFBibTeX XMLCite \textit{T. Tanisaki}, Nagoya Math. J. 214, 1--52 (2014; Zbl 1311.14047) Full Text: DOI arXiv
Tanisaki, Toshiyuki Differential operators on quantized flag manifolds at roots of unity. (English) Zbl 1264.14067 Adv. Math. 230, No. 4-6, 2235-2294 (2012). Reviewer: Gwyn Bellamy (Glasgow) MSC: 14M15 17B37 14F10 14A22 32C38 PDFBibTeX XMLCite \textit{T. Tanisaki}, Adv. Math. 230, No. 4--6, 2235--2294 (2012; Zbl 1264.14067) Full Text: DOI arXiv
Fang, Xin Quantum groups, \(q\)-boson algebras and quantized Weyl algebras. (English) Zbl 1238.16029 Int. J. Math. 22, No. 5, 675-694 (2011). Reviewer: Volodymyr Mazorchuk (Uppsala) MSC: 16T20 17B37 81R50 16S36 PDFBibTeX XMLCite \textit{X. Fang}, Int. J. Math. 22, No. 5, 675--694 (2011; Zbl 1238.16029) Full Text: DOI arXiv
Varagnolo, M.; Vasserot, E. Double affine Hecke algebras at roots of unity. (English) Zbl 1280.20005 Represent. Theory 14, 510-600 (2010). Reviewer: Hu Jun (Sydney) MSC: 20C08 14F05 17B37 16D90 PDFBibTeX XMLCite \textit{M. Varagnolo} and \textit{E. Vasserot}, Represent. Theory 14, 510--600 (2010; Zbl 1280.20005) Full Text: DOI arXiv
Masuoka, Akira Generalized \(q\)-boson algebras and their integrable modules. (English) Zbl 1213.17016 J. Algebra 322, No. 6, 2199-2219 (2009). MSC: 17B37 PDFBibTeX XMLCite \textit{A. Masuoka}, J. Algebra 322, No. 6, 2199--2219 (2009; Zbl 1213.17016) Full Text: DOI arXiv
Kolb, Stefan Quantum symmetric pairs and the reflection equation. (English) Zbl 1190.17007 Algebr. Represent. Theory 11, No. 6, 519-544 (2008). Reviewer: Sorin Dascalescu (Bucureşti) MSC: 17B37 PDFBibTeX XMLCite \textit{S. Kolb}, Algebr. Represent. Theory 11, No. 6, 519--544 (2008; Zbl 1190.17007) Full Text: DOI arXiv
Golubeva, V. A. Inverse monodromy problems in mathematical physics. (English. Russian original) Zbl 1178.32010 J. Math. Sci., New York 144, No. 1, 3775-3781 (2007); translation from Sovrem. Mat. Prilozh. 33 (2005). MSC: 32G34 82B26 PDFBibTeX XMLCite \textit{V. A. Golubeva}, J. Math. Sci., New York 144, No. 1, 3775--3781 (2007; Zbl 1178.32010); translation from Sovrem. Mat. Prilozh. 33 (2005) Full Text: DOI
Tanisaki, Toshiyuki The Beilinson-Bernstein correspondence for quantized enveloping algebras. (English) Zbl 1082.17010 Math. Z. 250, No. 2, 299-361 (2005). Reviewer: Zhang Hechun (Beijing) MSC: 17B37 16S32 PDFBibTeX XMLCite \textit{T. Tanisaki}, Math. Z. 250, No. 2, 299--361 (2005; Zbl 1082.17010) Full Text: DOI arXiv Backlinks: MO
Caldero, Ph. A multiplicative property of quantum flag minors. (English) Zbl 1030.17009 Represent. Theory 7, 164-176 (2003). MSC: 17B37 17B10 PDFBibTeX XMLCite \textit{Ph. Caldero}, Represent. Theory 7, 164--176 (2003; Zbl 1030.17009) Full Text: arXiv
Caldero, Philippe Toric degenerations of Schubert varieties. (English) Zbl 1050.14040 Transform. Groups 7, No. 1, 51-60 (2002). MSC: 14M15 14M25 14D06 PDFBibTeX XMLCite \textit{P. Caldero}, Transform. Groups 7, No. 1, 51--60 (2002; Zbl 1050.14040) Full Text: DOI arXiv
Caldero, Philippe On harmonic elements for semi-simple Lie algebras. (English) Zbl 0997.17009 Adv. Math. 166, No. 1, 73-99 (2002). Reviewer: Richard M.Green (Lancaster) MSC: 17B37 17B35 PDFBibTeX XMLCite \textit{P. Caldero}, Adv. Math. 166, No. 1, 73--99 (2002; Zbl 0997.17009) Full Text: DOI arXiv
Kamita, Atsushi Quantum \(b\)-functions of prehomogeneous vector spaces of commutative parabolic type. (English) Zbl 1022.11062 J. Algebra 244, No. 2, 581-603 (2001). Reviewer: Hiroshi Hosokawa (Yokohama) MSC: 11S90 14M17 PDFBibTeX XMLCite \textit{A. Kamita}, J. Algebra 244, No. 2, 581--603 (2001; Zbl 1022.11062) Full Text: DOI arXiv
Jimbo, M.; Konno, H.; Odake, S.; Shiraishi, J. Quasi-Hopf twistors for elliptic quantum groups. (English) Zbl 0977.17012 Transform. Groups 4, No. 4, 303-327 (1999). Reviewer: Tomasz Brzezinski (Swansea) MSC: 17B37 16W30 PDFBibTeX XMLCite \textit{M. Jimbo} et al., Transform. Groups 4, No. 4, 303--327 (1999; Zbl 0977.17012) Full Text: DOI arXiv
Gavarini, Fabio A PBW basis for Lusztig’s form of untwisted affine quantum groups. (English) Zbl 1014.17016 Commun. Algebra 27, No. 2, 903-918 (1999). MSC: 17B37 81R50 PDFBibTeX XMLCite \textit{F. Gavarini}, Commun. Algebra 27, No. 2, 903--918 (1999; Zbl 1014.17016) Full Text: DOI arXiv Link
Hayaishi, Norifumi; Miki, Kei \(L\) operators and Drinfeld’s generators. (English) Zbl 1056.17500 J. Math. Phys. 39, No. 3, 1623-1636 (1998). MSC: 17B37 17B67 PDFBibTeX XMLCite \textit{N. Hayaishi} and \textit{K. Miki}, J. Math. Phys. 39, No. 3, 1623--1636 (1998; Zbl 1056.17500) Full Text: DOI arXiv
Caldero, Philippe On the \(q\)-commutations in \(U_q({\mathfrak n})\) at roots of one. (English) Zbl 0929.17014 J. Algebra 210, No. 2, 557-576 (1998). Reviewer: Dražen Adamović (Zagreb) MSC: 17B37 16W35 PDFBibTeX XMLCite \textit{P. Caldero}, J. Algebra 210, No. 2, 557--576 (1998; Zbl 0929.17014) Full Text: DOI
Damiani, Ilaria The \(R\)-matrix for quantum algebras of non-twisted affine type. (La \(R\)-matrice pour les algèbres quantiques de type affine non tordu.) (French) Zbl 0911.17005 Ann. Sci. Éc. Norm. Supér. (4) 31, No. 4, 493-523 (1998). Reviewer: Sorin Dascalescu (Bucureşti) MSC: 17B37 PDFBibTeX XMLCite \textit{I. Damiani}, Ann. Sci. Éc. Norm. Supér. (4) 31, No. 4, 493--523 (1998; Zbl 0911.17005) Full Text: DOI Numdam EuDML
Akasaka, Tatsuya; Kashiwara, Masaki Finite-dimensional representations of quantum affine algebras. (English) Zbl 0915.17011 Publ. Res. Inst. Math. Sci. 33, No. 5, 839-867 (1997). Reviewer: A.N.Pressley (London) MSC: 17B37 17B67 PDFBibTeX XMLCite \textit{T. Akasaka} and \textit{M. Kashiwara}, Publ. Res. Inst. Math. Sci. 33, No. 5, 839--867 (1997; Zbl 0915.17011) Full Text: DOI arXiv
Frønsdal, Christian Generalization and exact deformations of quantum groups. (English) Zbl 0899.16021 Publ. Res. Inst. Math. Sci. 33, No. 1, 91-149 (1997). Reviewer: A.A.Bogush (Minsk) MSC: 16W30 17B37 17B67 81R50 16S80 PDFBibTeX XMLCite \textit{C. Frønsdal}, Publ. Res. Inst. Math. Sci. 33, No. 1, 91--149 (1997; Zbl 0899.16021) Full Text: DOI
Guizzi, Valentina A classification of unitary highest weight modules of the quantum analogue of the symmetric pair \((A_n,A_{n-1})\). (English) Zbl 0973.17017 J. Algebra 192, No. 1, 102-129 (1997). MSC: 17B37 17B10 PDFBibTeX XMLCite \textit{V. Guizzi}, J. Algebra 192, No. 1, 102--129 (1997; Zbl 0973.17017) Full Text: DOI
Hodges, Timothy J.; Levasseur, Thierry; Toro, Margarita Algebraic structure of multiparameter quantum groups. (English) Zbl 0878.17009 Adv. Math. 126, No. 1, 52-92 (1997). Reviewer: W.M.McGovern (Seattle) MSC: 17B37 16W30 PDFBibTeX XMLCite \textit{T. J. Hodges} et al., Adv. Math. 126, No. 1, 52--92 (1997; Zbl 0878.17009) Full Text: DOI arXiv
Etingof, Pavel I.; Kirillov, Alexander A. jun. Representation-theoretic proof of the inner product and symmetry identities for Macdonald’s polynomials. (English) Zbl 0859.17005 Compos. Math. 102, No. 2, 179-202 (1996). Reviewer: Stefano Capparelli (Roma) MSC: 17B37 05E05 PDFBibTeX XMLCite \textit{P. I. Etingof} and \textit{A. A. Kirillov jun.}, Compos. Math. 102, No. 2, 179--202 (1996; Zbl 0859.17005) Full Text: arXiv Numdam EuDML
Sugitani, Tetsuya Harmonic analysis on quantum spheres associated with representations of \(U_ q ({\mathfrak {so}}_ N)\) and \(q\)-Jacobi polynomials. (English) Zbl 0872.17013 Compos. Math. 99, No. 3, 249-281 (1995). MSC: 17B37 33D55 43A99 33D80 PDFBibTeX XMLCite \textit{T. Sugitani}, Compos. Math. 99, No. 3, 249--281 (1995; Zbl 0872.17013) Full Text: Numdam EuDML
Lyubashenko, Volodymyr V. Invariants of 3-manifolds and projective representations of mapping class groups via quantum groups at roots of unity. (English) Zbl 0844.57016 Commun. Math. Phys. 172, No. 3, 467-516 (1995). MSC: 57N10 17B37 PDFBibTeX XMLCite \textit{V. V. Lyubashenko}, Commun. Math. Phys. 172, No. 3, 467--516 (1995; Zbl 0844.57016) Full Text: DOI arXiv
Lyubashenko, Volodimir Existence of \(R\)-matrix for a quantized Kac-Moody algebra. (English) Zbl 1009.17504 Math. Proc. Camb. Philos. Soc. 116, No. 2, 193-207 (1994). Reviewer: Seok-Jin Kang (Soul) MSC: 17B37 17B67 16W30 81R50 82B23 PDFBibTeX XMLCite \textit{V. Lyubashenko}, Math. Proc. Camb. Philos. Soc. 116, No. 2, 193--207 (1994; Zbl 1009.17504) Full Text: DOI
Nakashima, Toshiki Quantum \(R\)-matrix and intertwiners for the Kashiwara algebra. (English) Zbl 0806.17011 Commun. Math. Phys. 164, No. 2, 239-258 (1994). MSC: 17B37 17B69 PDFBibTeX XMLCite \textit{T. Nakashima}, Commun. Math. Phys. 164, No. 2, 239--258 (1994; Zbl 0806.17011) Full Text: DOI arXiv
Yamane, Hiroyuki A Serre type theorem for affine Lie superalgebras and their quantized enveloping superalgebras. (English) Zbl 0987.17008 Proc. Japan Acad., Ser. A 70, No. 1, 31-36 (1994). Reviewer: O.Ninnemann (Berlin) MSC: 17B37 17B67 16W30 81R50 PDFBibTeX XMLCite \textit{H. Yamane}, Proc. Japan Acad., Ser. A 70, No. 1, 31--36 (1994; Zbl 0987.17008) Full Text: DOI Euclid
Matsuo, Atsushi Quantum algebra structure of certain Jackson integrals. (English) Zbl 0795.17023 Commun. Math. Phys. 157, No. 3, 479-498 (1993). MSC: 17B37 33D80 17B69 PDFBibTeX XMLCite \textit{A. Matsuo}, Commun. Math. Phys. 157, No. 3, 479--498 (1993; Zbl 0795.17023) Full Text: DOI