Nonabelian theta functions of positive genus

Boysal, Arzu

doi:10.1090/S0002-9939-08-09467-7

Nonabelian theta functions of positive genus
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References

Arnaud Beauville, Conformal blocks, fusion rules and the Verlinde formula, Proceedings of the Hirzebruch 65 Conference on Algebraic Geometry (Ramat Gan, 1993) Israel Math. Conf. Proc., vol. 9, Bar-Ilan Univ., Ramat Gan, 1996, pp. 75–96. MR 1360497
Arnaud Beauville and Yves Laszlo, Conformal blocks and generalized theta functions, Comm. Math. Phys. 164 (1994), no. 2, 385–419. MR 1289330
Usha Bhosle and A. Ramanathan, Moduli of parabolic $G$-bundles on curves, Math. Z. 202 (1989), no. 2, 161–180. MR 1013082, DOI 10.1007/BF01215252
Nicolas Bourbaki, Éléments de mathématique, Masson, Paris, 1981 (French). Groupes et algèbres de Lie. Chapitres 4, 5 et 6. [Lie groups and Lie algebras. Chapters 4, 5 and 6]. MR 647314
J.-M. Drezet and M. S. Narasimhan, Groupe de Picard des variétés de modules de fibrés semi-stables sur les courbes algébriques, Invent. Math. 97 (1989), no. 1, 53–94 (French). MR 999313, DOI 10.1007/BF01850655
Gerd Faltings, A proof for the Verlinde formula, J. Algebraic Geom. 3 (1994), no. 2, 347–374. MR 1257326
Gerd Faltings, Stable $G$-bundles and projective connections, J. Algebraic Geom. 2 (1993), no. 3, 507–568. MR 1211997
William Fulton, Eigenvalues, invariant factors, highest weights, and Schubert calculus, Bull. Amer. Math. Soc. (N.S.) 37 (2000), no. 3, 209–249. MR 1754641, DOI 10.1090/S0273-0979-00-00865-X
Morikuni Gotô, A theorem on compact semi-simple groups, J. Math. Soc. Japan 1 (1949), 270–272. MR 33829, DOI 10.2969/jmsj/00130270
Victor G. Kac, Infinite-dimensional Lie algebras, 3rd ed., Cambridge University Press, Cambridge, 1990. MR 1104219, DOI 10.1017/CBO9780511626234
Allen Knutson and Terence Tao, Honeycombs and sums of Hermitian matrices, Notices Amer. Math. Soc. 48 (2001), no. 2, 175–186. MR 1811121
Shrawan Kumar, Proof of the Parthasarathy-Ranga Rao-Varadarajan conjecture, Invent. Math. 93 (1988), no. 1, 117–130. MR 943925, DOI 10.1007/BF01393689
Shrawan Kumar, M. S. Narasimhan, and A. Ramanathan, Infinite Grassmannians and moduli spaces of $G$-bundles, Math. Ann. 300 (1994), no. 1, 41–75. MR 1289830, DOI 10.1007/BF01450475
Yves Laszlo and Christoph Sorger, The line bundles on the moduli of parabolic $G$-bundles over curves and their sections, Ann. Sci. École Norm. Sup. (4) 30 (1997), no. 4, 499–525 (English, with English and French summaries). MR 1456243, DOI 10.1016/S0012-9593(97)89929-6
Olivier Mathieu, Construction d’un groupe de Kac-Moody et applications, Compositio Math. 69 (1989), no. 1, 37–60 (French). MR 986812
V. B. Mehta and C. S. Seshadri, Moduli of vector bundles on curves with parabolic structures, Math. Ann. 248 (1980), no. 3, 205–239. MR 575939, DOI 10.1007/BF01420526
Christian Pauly, Espaces de modules de fibrés paraboliques et blocs conformes, Duke Math. J. 84 (1996), no. 1, 217–235 (French). MR 1394754, DOI 10.1215/S0012-7094-96-08408-2
Christoph Sorger, La formule de Verlinde, Astérisque 237 (1996), Exp. No. 794, 3, 87–114 (French, with French summary). Séminaire Bourbaki, Vol. 1994/95. MR 1423621
C. Teleman and C. Woodward, Parabolic bundles, products of conjugacy classes and Gromov-Witten invariants, Ann. Inst. Fourier (Grenoble) 53 (2003), no. 3, 713–748 (English, with English and French summaries). MR 2008438
Akihiro Tsuchiya, Kenji Ueno, and Yasuhiko Yamada, Conformal field theory on universal family of stable curves with gauge symmetries, Integrable systems in quantum field theory and statistical mechanics, Adv. Stud. Pure Math., vol. 19, Academic Press, Boston, MA, 1989, pp. 459–566. MR 1048605, DOI 10.2969/aspm/01910459
Erik Verlinde, Fusion rules and modular transformations in $2$D conformal field theory, Nuclear Phys. B 300 (1988), no. 3, 360–376. MR 954762, DOI 10.1016/0550-3213(88)90603-7