Representations of Hecke algebras
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- by Eugene Gutkin PDF
- Trans. Amer. Math. Soc. 309 (1988), 269-277 Request permission
Abstract:
We find all operators of a certain type that satisfy the braid relations corresponding to any generalized Cartan matrix.References
- Alberto Arabia, Cohomologie $\textbf {T}$-équivariante de $\textbf {G}/\textbf {B}$ pour un groupe $\textbf {G}$ de Kac-Moody, C. R. Acad. Sci. Paris Sér. I Math. 302 (1986), no. 17, 631–634 (French, with English summary). MR 845656 J. Bernstein, Letter, 1986.
- I. N. Bernšteĭn, I. M. Gel′fand, and S. I. Gel′fand, Schubert cells, and the cohomology of the spaces $G/P$, Uspehi Mat. Nauk 28 (1973), no. 3(171), 3–26 (Russian). MR 0429933
- N. Bourbaki, Éléments de mathématique. Fasc. XXXIV. Groupes et algèbres de Lie. Chapitre IV: Groupes de Coxeter et systèmes de Tits. Chapitre V: Groupes engendrés par des réflexions. Chapitre VI: systèmes de racines, Actualités Scientifiques et Industrielles [Current Scientific and Industrial Topics], No. 1337, Hermann, Paris, 1968 (French). MR 0240238
- Michel Demazure, Invariants symétriques entiers des groupes de Weyl et torsion, Invent. Math. 21 (1973), 287–301 (French). MR 342522, DOI 10.1007/BF01418790
- Michel Demazure, Désingularisation des variétés de Schubert généralisées, Ann. Sci. École Norm. Sup. (4) 7 (1974), 53–88 (French). MR 354697
- Sam Evens and Paul Bressler, On certain Hecke rings, Proc. Nat. Acad. Sci. U.S.A. 84 (1987), no. 3, 624–625. MR 873070, DOI 10.1073/pnas.84.3.624
- Eugene Gutkin, Integrable systems with delta-potential, Duke Math. J. 49 (1982), no. 1, 1–21. MR 650365
- Eugene Gutkin, Operator calculi associated with reflection groups, Duke Math. J. 55 (1987), no. 1, 1–18. MR 883660, DOI 10.1215/S0012-7094-87-05501-3
- Eugene Gutkin, Schubert calculus on flag varieties of Kac-Moody groups, Algebras Groups Geom. 3 (1986), no. 1, 27–59. MR 861861
- Eugene Gutkin and Peter Slodowy, Cohomologie des variétés de drapeaux infinies, C. R. Acad. Sci. Paris Sér. I Math. 296 (1983), no. 15, 625–627 (French, with English summary). MR 705676
- Victor G. Kac, Infinite-dimensional Lie algebras, Progress in Mathematics, vol. 44, Birkhäuser Boston, Inc., Boston, MA, 1983. An introduction. MR 739850, DOI 10.1007/978-1-4757-1382-4 V. Kac and D. Peterson, Cohomology of infinite dimensional groups and their flag varieties (to appear).
- Bertram Kostant and Shrawan Kumar, The nil Hecke ring and cohomology of $G/P$ for a Kac-Moody group $G$, Proc. Nat. Acad. Sci. U.S.A. 83 (1986), no. 6, 1543–1545. MR 831908, DOI 10.1073/pnas.83.6.1543 G. Luszting, Equivariant $K$-theory and representations of Hecke algebras, Proc. Amer. Math. Soc. 94 (1985), 337-342.
Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 309 (1988), 269-277
- MSC: Primary 22E30; Secondary 17B67
- DOI: https://doi.org/10.1090/S0002-9947-1988-0957070-0
- MathSciNet review: 957070