Nakajima, Hiraku; Weekes, Alex Coulomb branches of quiver gauge theories with symmetrizers. (English) Zbl 1508.14011 J. Eur. Math. Soc. (JEMS) 25, No. 1, 203-230 (2023). Reviewer: Mee Seong Im (Annapolis) MSC: 14D21 16G20 17B37 81T13 PDFBibTeX XMLCite \textit{H. Nakajima} and \textit{A. Weekes}, J. Eur. Math. Soc. (JEMS) 25, No. 1, 203--230 (2023; Zbl 1508.14011) Full Text: DOI arXiv
Nakajima, Hiraku Euler numbers of Hilbert schemes of points on simple surface singularities and quantum dimensions of standard modules of quantum affine algebras. (English) Zbl 1467.14011 Kyoto J. Math. 61, No. 2, 377-397 (2021). MSC: 14C05 14D21 17B37 PDFBibTeX XMLCite \textit{H. Nakajima}, Kyoto J. Math. 61, No. 2, 377--397 (2021; Zbl 1467.14011) Full Text: DOI arXiv
Nakajima, Hiraku Introduction to a provisional mathematical definition of Coulomb branches of 3-dimensional \(\mathcal{N}=4\) gauge theories. (English) Zbl 1471.22020 Muñoz, Vicente (ed.) et al., Modern geometry. A celebration of the work of Simon Donaldson. Providence, RI: American Mathematical Society (AMS). Proc. Symp. Pure Math. 99, 193-211 (2018). MSC: 22E70 14D21 55N91 PDFBibTeX XMLCite \textit{H. Nakajima}, Proc. Symp. Pure Math. 99, 193--211 (2018; Zbl 1471.22020) Full Text: DOI arXiv
Nakajima, Hiraku Introduction to quiver varieties – for ring and representation theorists. (English) Zbl 1437.17007 Ueda, Akira (ed.), Proceedings of the 49th symposium on ring theory and representation theory, Osaka Prefecture University, Osaka, Japan, August 31 – September 3, 2016. Shimane: Symposium on Ring Theory and Representation Theory Organizing Committee. 96-114 (2017). Reviewer: Olaf Ninnemann (Uffing am Staffelsee) MSC: 17B37 17B67 16G20 14D21 PDFBibTeX XMLCite \textit{H. Nakajima}, in: Proceedings of the 49th symposium on ring theory and representation theory, Osaka Prefecture University, Osaka, Japan, August 31 -- September 3, 2016. Shimane: Symposium on Ring Theory and Representation Theory Organizing Committee. 96--114 (2017; Zbl 1437.17007) Full Text: arXiv
Nakajima, Hiraku Lectures on perverse sheaves on instanton moduli spaces. (English) Zbl 1403.14036 Bezrukavnikov, Roman (ed.) et al., Geometry of moduli spaces and representation theory. Lecture notes from the 2015 IAS/Park City Mathematics Institute (PCMI) Graduate Summer School, Park City, UT, USA, June 28 – July 18, 2015. Providence, RI: American Mathematical Society (AMS); Princeton, NJ: Institute for Advanced Study (IAS) (ISBN 978-1-4704-3574-5/hbk; 978-1-4704-4234-7/ebook). IAS/Park City Mathematics Series 24, 381-436 (2017). MSC: 14D21 14J60 17B69 14-02 PDFBibTeX XMLCite \textit{H. Nakajima}, IAS/Park City Math. Ser. 24, 381--436 (2017; Zbl 1403.14036) Full Text: arXiv
Nakajima, Hiraku; Takayama, Yuuya Cherkis bow varieties and Coulomb branches of quiver gauge theories of affine type \(A\). (English) Zbl 1431.16014 Sel. Math., New Ser. 23, No. 4, 2553-2633 (2017). MSC: 16G20 14D21 81T13 PDFBibTeX XMLCite \textit{H. Nakajima} and \textit{Y. Takayama}, Sel. Math., New Ser. 23, No. 4, 2553--2633 (2017; Zbl 1431.16014) Full Text: DOI arXiv
Nakajima, Hiraku More lectures on Hilbert schemes of points on surfaces. (English) Zbl 1369.14012 Fujino, Osamu (ed.) et al., Development of moduli theory – Kyoto 2013. Proceedings of the 6th Mathematical Society of Japan-Seasonal Institute, MSJ-SI, Kyoto, Japan, June 11–21, 2013. Tokyo: Mathematical Society of Japan (MSJ) (ISBN 978-4-86497-032-7/hbk). Advanced Studies in Pure Mathematics 69, 173-205 (2016). MSC: 14C05 14D21 14J60 PDFBibTeX XMLCite \textit{H. Nakajima}, Adv. Stud. Pure Math. 69, 173--205 (2016; Zbl 1369.14012) Full Text: arXiv
Braverman, Alexander; Finkelberg, Michael; Nakajima, Hiraku Instanton moduli spaces and \(\mathcal W\)-algebras. (English) Zbl 1435.14001 Astérisque 385. Paris: Société Mathématique de France (SMF) (ISBN 978-2-85629-848-0/pbk). vii, 128 p. (2016). Reviewer: Oleksandr Iena (München) MSC: 14-02 17-02 14D21 14D20 14F43 17B69 17B68 14J60 14C05 PDFBibTeX XMLCite \textit{A. Braverman} et al., Instanton moduli spaces and \(\mathcal W\)-algebras. Paris: Société Mathématique de France (SMF) (2016; Zbl 1435.14001) Full Text: arXiv
Braverman, Alexander; Finkelberg, Michael; Nakajima, Hiraku Coulomb branches of \(3d\) \(\mathcal N=4\) quiver gauge theories and slices in the affine Grassmannian (with appendices by Alexander Braverman, Michael Finkelberg, Joel Kamnitzer, Ryosuke Kodera, Hiraku Nakajima, Ben Webster, and Alex Weekes). arXiv:1604.03625 Preprint, arXiv:1604.03625 [math.RT] (2016). MSC: 81T13 14D21 16G20 20G45 BibTeX Cite \textit{A. Braverman} et al., ``Coulomb branches of $3d$ $\mathcal N=4$ quiver gauge theories and slices in the affine Grassmannian (with appendices by Alexander Braverman, Michael Finkelberg, Joel Kamnitzer, Ryosuke Kodera, Hiraku Nakajima, Ben Webster, and Alex Weekes)'', Preprint, arXiv:1604.03625 [math.RT] (2016) Full Text: arXiv OA License
Nakajima, Hiraku Refined Chern-Simons theory and Hilbert schemes of points on the plane. (English) Zbl 1298.14008 Etingof, Pavel (ed.) et al., Perspectives in representation theory. A conference in honor of Igor Frenkel’s 60th birthday on perspectives in representation theory, Yale University, New Haven, CT, USA, May 12–17, 2012. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-9170-4/pbk; 978-1-4704-1523-5/ebook). Contemporary Mathematics 610, 305-331 (2014). Reviewer: Scott Nollet (Fort Worth) MSC: 14C05 33D52 14D21 PDFBibTeX XMLCite \textit{H. Nakajima}, Contemp. Math. 610, 305--331 (2014; Zbl 1298.14008) Full Text: arXiv
Nakajima, Hiraku Handsaw quiver varieties and finite \(W\)-algebras. (English) Zbl 1290.17013 Mosc. Math. J. 12, No. 3, 633-666 (2012). MSC: 17B37 14D21 PDFBibTeX XMLCite \textit{H. Nakajima}, Mosc. Math. J. 12, No. 3, 633--666 (2012; Zbl 1290.17013) Full Text: arXiv Link
Nakajima, Hiraku; Yoshioka, Kota Perverse coherent sheaves on blow-up. I. A quiver description. (English) Zbl 1247.14009 Hasegawa, Koji (ed.) et al., Exploring new structures and natural constructions in mathematical physics. Collected papers of the conference upon the occasion of the retirement of Professor Akihiro Tsuchiya, Nagoya, Japan, March 5–8, 2007. Tokyo: Mathematical Society of Japan (ISBN 978-4-931469-64-8/hbk). Advanced Studies in Pure Mathematics 61, 349-386 (2011). Reviewer: Xueqing Chen (Whitewater) MSC: 14D21 81T30 81R10 53A20 32L10 PDFBibTeX XMLCite \textit{H. Nakajima} and \textit{K. Yoshioka}, Adv. Stud. Pure Math. 61, 349--386 (2011; Zbl 1247.14009) Full Text: arXiv
Nagao, Kentaro; Nakajima, Hiraku Counting invariant of perverse coherent sheaves and its wall-crossing. (English) Zbl 1250.14021 Int. Math. Res. Not. 2011, No. 17, 3885-3938 (2011). Reviewer: Jason Lo (Columbia) MSC: 14J10 14D21 14D23 14J30 14J60 14F05 PDFBibTeX XMLCite \textit{K. Nagao} and \textit{H. Nakajima}, Int. Math. Res. Not. 2011, No. 17, 3885--3938 (2011; Zbl 1250.14021) Full Text: DOI arXiv
Nakajima, Hiraku; Yoshioka, Kōta Perverse coherent sheaves on blowup. III: Blow-up formula from wall-crossing. (English) Zbl 1220.14012 Kyoto J. Math. 51, No. 2, 263-335 (2011). Reviewer: Markus Szymik (Bochum) MSC: 14D21 16G20 PDFBibTeX XMLCite \textit{H. Nakajima} and \textit{K. Yoshioka}, Kyoto J. Math. 51, No. 2, 263--335 (2011; Zbl 1220.14012) Full Text: DOI arXiv
Göttsche, Lothar; Nakajima, Hiraku; Yoshioka, Kota Donaldson = Seiberg-Witten from Mochizuki’s formula and instanton counting. (English) Zbl 1259.14046 Publ. Res. Inst. Math. Sci. 47, No. 1, 307-359 (2011). Reviewer: Hans U. Boden (Hamilton/Ontario) MSC: 14J80 14D21 57R57 PDFBibTeX XMLCite \textit{L. Göttsche} et al., Publ. Res. Inst. Math. Sci. 47, No. 1, 307--359 (2011; Zbl 1259.14046) 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 PDFBibTeX XMLCite \textit{H. Nakajima}, Kyoto J. Math. 51, No. 1, 71--126 (2011; Zbl 1223.13013) Full Text: DOI arXiv
Nakajima, Hiraku \(t\)-analogs of \(q\)-characters of quantum affine algebras of type \(E_6\), \(E_7\), \(E_8\). (English) Zbl 1259.17015 Gyoja, Akihiko (ed.) et al., Representation theory of algebraic groups and quantum groups. Based on the 6th international conference by the Graduate School of Mathematics on representation theory of algebraic groups and quantum groups, Nagoya, Japan, June 12–17, 2006. Boston, MA: Birkhäuser (ISBN 978-0-8176-4696-7/hbk; 978-0-8176-4697-4/ebook). Progress in Mathematics 284, 257-272 (2010). MSC: 17B37 14D21 16G20 PDFBibTeX XMLCite \textit{H. Nakajima}, Prog. Math. 284, 257--272 (2010; Zbl 1259.17015) Full Text: DOI arXiv
Nakajima, Hiraku; Yoshioka, Kōda Instanton counting and Donaldson invariants. (English. Japanese original) Zbl 1225.14010 Sugaku Expo. 23, No. 2, 189-212 (2010); translation from Sūgaku 59, No. 2, 131-153 (2007). Reviewer: Vehbi Emrah Paksoy (Fort Lauderdale) MSC: 14D21 57M27 14N35 PDFBibTeX XMLCite \textit{H. Nakajima} and \textit{K. Yoshioka}, Sugaku Expo. 23, No. 2, 189--212 (2010; Zbl 1225.14010); translation from Sūgaku 59, No. 2, 131--153 (2007) Full Text: Link
Göttsche, Lothar; Nakajima, Hiraku; Yoshioka, Kōta \(K\)-theoretic Donaldson invariants via instanton counting. (English) Zbl 1192.14011 Pure Appl. Math. Q. 5, No. 3, 1029-1111 (2009). Reviewer: Zhenbo Qin (Columbia) MSC: 14D21 57R57 81T13 PDFBibTeX XMLCite \textit{L. Göttsche} et al., Pure Appl. Math. Q. 5, No. 3, 1029--1111 (2009; Zbl 1192.14011) Full Text: DOI arXiv
Nakajima, Hiraku Quiver varieties and branching. (English) Zbl 1241.17028 SIGMA, Symmetry Integrability Geom. Methods Appl. 5, Paper 003, 37 p. (2009). MSC: 17B67 14D21 14F43 20G44 PDFBibTeX XMLCite \textit{H. Nakajima}, SIGMA, Symmetry Integrability Geom. Methods Appl. 5, Paper 003, 37 p. (2009; Zbl 1241.17028) Full Text: DOI arXiv
Nakajima, Hiraku Sheaves on ALE spaces and quiver varieties. (English) Zbl 1166.14007 Mosc. Math. J. 7, No. 4, 699-722 (2007). MSC: 14D21 53C26 16G20 PDFBibTeX XMLCite \textit{H. Nakajima}, Mosc. Math. J. 7, No. 4, 699--722 (2007; Zbl 1166.14007)
Nakajima, Hiraku Quiver varieties and quantum affine algebras. (English. Japanese original) Zbl 1246.17021 Sugaku Expo. 19, No. 1, 53-78 (2006); translation from Sūgaku 52, No. 4, 337-359 (2000). Reviewer: Olaf Ninnemann (Berlin) MSC: 17B37 14D21 14L30 16G20 33D80 PDFBibTeX XMLCite \textit{H. Nakajima}, Sugaku Expo. 19, No. 1, 53--78 (2006; Zbl 1246.17021); translation from Sūgaku 52, No. 4, 337--359 (2000)
Nakajima, Hiraku; Yoshioka, Kota Instanton counting on blowup. II: \(K\)-theoretic partition function. (English) Zbl 1110.14015 Transform. Groups 10, No. 3-4, 489-519 (2005). MSC: 14D21 14C35 53D20 53D45 57R57 81T60 81T13 83E15 PDFBibTeX XMLCite \textit{H. Nakajima} and \textit{K. Yoshioka}, Transform. Groups 10, No. 3--4, 489--519 (2005; Zbl 1110.14015) Full Text: DOI arXiv
Nakajima, Hiraku; Yoshioka, Kota Instanton counting on blowup. I: 4-dimensional pure gauge theory. (English) Zbl 1100.14009 Invent. Math. 162, No. 2, 313-355 (2005). Reviewer: Bernd Kreußler (Limerick) MSC: 14D21 57R57 81T13 81T60 14J80 PDFBibTeX XMLCite \textit{H. Nakajima} and \textit{K. Yoshioka}, Invent. Math. 162, No. 2, 313--355 (2005; Zbl 1100.14009) Full Text: DOI arXiv
Nakajima, Hiraku; Yoshioka, Kōta Lectures on instanton counting. (English) Zbl 1080.14016 Hurtubise, Jacques (ed.) et al., Algebraic structures and moduli spaces. Proceedings of the CRM workshop, Montréal, Canada, July 14-20, 2003. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-3568-8/pbk). CRM Proceedings & Lecture Notes 38, 31-101 (2004). Reviewer: Zhenbo Qin (Columbia) MSC: 14D21 14J81 14N35 57R57 81T13 81T60 PDFBibTeX XMLCite \textit{H. Nakajima} and \textit{K. Yoshioka}, CRM Proc. Lect. Notes 38, 31--101 (2004; Zbl 1080.14016) Full Text: arXiv
Nakajima, Hiraku Reflection functors for quiver varieties and Weyl group actions. (English) Zbl 1060.16017 Math. Ann. 327, No. 4, 671-721 (2003). Reviewer: Domenico Fiorenza (Roma) MSC: 16G20 53C26 14D21 20F55 33D80 PDFBibTeX XMLCite \textit{H. Nakajima}, Math. Ann. 327, No. 4, 671--721 (2003; Zbl 1060.16017) Full Text: DOI
Nakajima, Hiraku Geometric construction of representations of affine algebras. (English) Zbl 1049.17014 Li, Ta Tsien (ed.) et al., Proceedings of the international congress of mathematicians, ICM 2002, Beijing, China, August 20–28, 2002. Vol. I: Plenary lectures and ceremonies. Beijing: Higher Education Press; Singapore: World Scientific/distributor (ISBN 7-04-008690-5/3 vol. set). 423-438 (2002). Reviewer: Ye Jiachen (Shanghai) MSC: 17B37 14D21 14L30 16G20 33D80 PDFBibTeX XMLCite \textit{H. Nakajima}, in: Proceedings of the international congress of mathematicians, ICM 2002, Beijing, China, August 20--28, 2002. Vol. I: Plenary lectures and ceremonies. Beijing: Higher Education Press; Singapore: World Scientific/distributor. 423--438 (2002; Zbl 1049.17014) Full Text: arXiv
Nakajima, Hiraku Quiver varieties and finite dimensional representations of quantum affine algebras. (English) Zbl 0981.17016 J. Am. Math. Soc. 14, No. 1, 145-238 (2001). Reviewer: Li Fang (Hangzhou) MSC: 17B37 14D21 14L30 16G20 33D80 PDFBibTeX XMLCite \textit{H. Nakajima}, J. Am. Math. Soc. 14, No. 1, 145--238 (2001; Zbl 0981.17016) Full Text: DOI arXiv
Asano, N.; Nakajima, H. Construction of the two-dimensional recursion operators. (English) Zbl 0941.37550 Boiti, M. (ed.) et al., Nonlinear evolution equations and dynamical systems. Proceedings of the 7th workshop, NEEDS ’91, Baia Verde, Italy, June 19-29, 1991. Singapore: World Scientific. 341-348 (1992). MSC: 37K35 35Q99 PDFBibTeX XMLCite \textit{N. Asano} and \textit{H. Nakajima}, in: Nonlinear evolution equations and dynamical systems. Proceedings of the 7th workshop, NEEDS '91, Baia Verde, Italy, June 19-29, 1991. Singapore: World Scientific. 341--348 (1992; Zbl 0941.37550)