Affine Hecke algebras and generalized standard young tableaux

Journal of Algebra

Volumn 260, Issue 1, 2003, Pages 367-415

  Ram, Arun ^a  

^a UNIVERSITY OF WISCONSIN MADISON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037309779     PISSN: 00218693     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0021-8693(02)00663-4     Document Type: Review

References (49)

1. n and construction of its irreducible representations, Adv. Math. 106 (1994) 216-243.
2. C. Athanasiadis, S. Linusson, A simple bijection for the regions of the Shi arrangement of hyperplanes, Discrete Math. 204 (1-3) (1999) 27-39.
3. M. Aubert, Dualité dans le groupe de Grothendieck de la categorie des représentations lisses de longueur finie d'un groupe réductif p-adique, Trans. Amer. Soc. 347 (1995) 2179-2189.
4. A. Björner, Orderings of Coxeter groups, in: Combinatorics and Algebra, Boulder, CO, 1983, Contemp. Math., Vol. 34, Amer. Math. Society, Providence, 1984, pp. 175-195.
5. A. Björner, M. Wachs, Generalized quotients in Coxeter groups, Trans. Amer. Math. Soc. 308 (1) (1988) 1-37.
6. N. Bourbaki, Groupes et algèbres de Lie, Chapitres 4, 5 et 6, Elements de Mathématique, Hermann, Paris, 1968.
7. R. Carter, G. Segal, I.G. Macdonald, Lectures on Lie Groups and Lie Algebras, London Math. Soc. Stud. Texts, Vol. 32, Cambridge Univ. Press, Cambridge, 1995.
8. N. Chriss, V. Ginzburg, Representation Theory and Complex Geometry, Birkhäuser, 1997.
9. A. Garsia, C. Reutenauer, A decomposition of Solomon's descent algebra, Adv. Math. 77 (2) (1989) 189-262.
10. P.N. Hoefsmit, Representations of Hecke algebras of finite groups with BN-pairs of classical type, PhD thesis, University of British Columbia, 1974.
11. N. Iwahori, H. Matsumoto, On some Bruhat decomposition and the structure of the Hecke rings of p-adic Chevalley groups, Publ. Math. Inst. Hautes Études Sci. 40 (1972) 81-116.
12. S. Kato, Irreducibility of principal series representations for Hecke algebras of affine type, J. Fac. Sci. Univ. Tokyo Sec. IA 28 (1981) 929-943.
13. S. Kato, Duality for representations of a Hecke algebra, Proc. Amer. Math. Soc. 119 (1993) 941-946.
14. D. Kazhdan, G. Lusztig, Proof of the Deligne-Langlands conjecture for Hecke algebras, Invent. Math. 87 (1987) 153-215.
15. B. Kostant, A generalization of the Bott-Borel-Weil theorem and Euler number multiplets of representations, Conference Moshé Flato 1999 (Dijon), Lett. Math. Phys. 52 (1) (2000) 61-78.
16. C. Krattenthaler, L. Orsina, P. Papi, Enumeration of ad-nilpotent b-ideals for simple Lie algebras, Adv. Appl. Math, Special issue in memory of Rodica Simion, to appear.
17. C. Kriloff, A. Ram, Representations of graded Hecke algebras, Represent. Theory 6 (2002) 31-69; http://www.ams.org/ert/home-2002.html.
18. H. Knight, A. Zelevinsky, Representations of quivers of type A and the multisegment duality, Adv. Math. 117 (2) (1996) 273-293.
19. B. Leclerc, J.-Y. Thibon, E. Vasserot, Zelevinsky's involution at roots of unity, J. Reine Angew. Math. 513 (1999) 33-51.
20. P. Littelmann, Paths and root operators in representation theory, Ann. of Math. (2) 142 (1995) 499-525.
21. P. Littelmann, The path model for representations of symmetrizable Kac-Moody algebras, in: Proceedings of the International Congress of Mathematicians, Vol. 1, Zürich, 1994, Birkhäuser, Basel, 1995, pp. 298-308.
22. J. Losonczy, Standard Young tableaux in the Weyl group setting, J. Algebra 220 (1999) 255-260.
23. G. Lusztig, Singularities, character formulas, and a q-analog of weight multiplicities, in: Analysis and Topology on Singular Spaces, II, III, Luminy, 1981, Astérisque 101-102 (1993) 208-229.
24. I.G. Macdonald, Symmetric Functions and Hall Polynomials, 2nd edition, Oxford Math. Monographs, Oxford Univ. Press, New York, 1995.
25. C. Moeglin, J.-L. Waldspurger, L'involution de Zelevinski, J. Reine Angew. Math. 372 (1986) 136-177.
26. M. Nazarov, V. Tarasov, Representations of Yangians with Gelfand-Zetlin bases, J. Reine Angew. Math. 496 (1998) 191-212.
27. A. Ram, Representations of rank two affine Hecke algebras, in: Advances in Algebra and Geometry (University of Hyderabad Conference 2001), Hidustan Book Agency, New Delhi, India, 2002, pp. 57-91.
28. A. Ram, Calibrated representations of affine Hecke algebras, Preprint, 1998, http://www.math.wisc.edu/~ram/preprints.html.
29. A. Ram, Standard Young tableaux for finite root systems, Preprint, 1998, http://www.math.wisc.edu/~ram/preprints.html.
30. A. Ram, J. Ramagge, Affine Hecke algebras, cyclotomic Hecke algebras and Clifford theory, to appear in: V. Lakshmibai, R. Sridharan (Eds.), A volume in honor of the 70th birthday of C.S. Seshadri, 2003.
31. C. Reutenauer, Free Lie Algebras, in: London Math. Soc. Monogr. (N.S.), Vol. 7, Oxford Univ. Press, New York, 1993.
32. J. Rogawski, On modules over the Hecke algebra of a p-adic group, Invent. Math. 79 (1985) 443-465.
33. J.-Y. Shi, The number of ⊕-sign types, Quart. J. Math. Oxford Ser. (2) 48 (1997) 93-105.
34. J.-Y. Shi, Left cells in affine Weyl groups, Tôhoku Math. J. (2) 46 (1) (1994) 105-124.
35. J.-Y. Shi, Sign types corresponding to an affine Weyl group, J. London Math. Soc. (2) 35 (1987) 56-74.
36. L. Solomon, A Mackey formula in the group ring of a Coxeter group, J. Algebra 41 (2) (1976) 255-264.
37. L. Solomon, H. Terao, The double Coxeter arrangement, Preprint, 1997.
38. R. Stanley, Hyperplane arrangements, interval orders, and trees, Proc. Nat. Acad. Sci. USA 93 (1996) 2620-2625.
39. R. Stanley, Hyperplane arrangements, parking functions and tree inversions, in: Mathematical Essays in Honor of Gian-Carlo Rota, Birkhäuser, Boston, 1998.
40. R. Steinberg, Lectures on Chevalley groups, Notes prepared by John Faulkner and Robert Wilson, Yale University, New Haven, CT, 1968.
41. R. Steinberg, Endomorphisms of linear algebraic groups, Mem. Amer. Math. Soc. 80 (1968) 1-108.
42. R. Steinberg, On a theorem of Pittie, Topology 14 (1975) 173-177.
43. S. Sundaram, Tableaux in the representation theory of the classical Lie groups, in: Invariant Theory and Tableaux, Minneapolis, MN, 1988, IMA Vol. Math. Appl., Vol. 19, Springer-Verlag, New York, 1990, pp.191-225.
44. N. Wallach, Real reductive groups I, Pure Appl. Math., Vol. 132, Academic Press, Boston, MA, 1988.
45. n and subfactors, Invent. Math. 92 (1988) 349-383.
46. N. Xi, Representations of Affine Hecke Algebras, Lecture Notes in Math., Vol. 1587, Springer-Verlag, Berlin, 1994.
47. A. Young, The Collected Papers of Alfred Young 1873-1940, Math. Expositions, Vol. 21, University of Toronto Press, 1977.
48. A. Young, On quantitative substitutional analysis (sixth paper), Proc. London. Math. Soc. (2) 34 (1931) 196-230.
49. A. Zelevinsky, Induced representations of p-adic groups II: On irreducible representations of GL(n), Ann. Sci. École Norm. Sup. (4) 13 (1980) 165-210.