Hecke algebra characters and immanant conjectures
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- by Mark Haiman
- J. Amer. Math. Soc. 6 (1993), 569-595
- DOI: https://doi.org/10.1090/S0894-0347-1993-1186961-9
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References
- Dan Barbasch and David Vogan, Primitive ideals and orbital integrals in complex exceptional groups, J. Algebra 80 (1983), no. 2, 350–382. MR 691809, DOI 10.1016/0021-8693(83)90006-6
- Alexandre Beĭlinson and Joseph Bernstein, Localisation de $g$-modules, C. R. Acad. Sci. Paris Sér. I Math. 292 (1981), no. 1, 15–18 (French, with English summary). MR 610137
- A. A. Beĭlinson, J. Bernstein, and P. Deligne, Faisceaux pervers, Analysis and topology on singular spaces, I (Luminy, 1981) Astérisque, vol. 100, Soc. Math. France, Paris, 1982, pp. 5–171 (French). MR 751966
- 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
- Francesco Brenti, Unimodal polynomials arising from symmetric functions, Proc. Amer. Math. Soc. 108 (1990), no. 4, 1133–1141. MR 993741, DOI 10.1090/S0002-9939-1990-0993741-2
- J.-L. Brylinski and M. Kashiwara, Kazhdan-Lusztig conjecture and holonomic systems, Invent. Math. 64 (1981), no. 3, 387–410. MR 632980, DOI 10.1007/BF01389272
- P. Freyd, D. Yetter, J. Hoste, W. B. R. Lickorish, K. Millett, and A. Ocneanu, A new polynomial invariant of knots and links, Bull. Amer. Math. Soc. (N.S.) 12 (1985), no. 2, 239–246. MR 776477, DOI 10.1090/S0273-0979-1985-15361-3
- Mark Goresky and Robert MacPherson, Intersection homology. II, Invent. Math. 72 (1983), no. 1, 77–129. MR 696691, DOI 10.1007/BF01389130
- I. P. Goulden and D. M. Jackson, Immanants of combinatorial matrices, J. Algebra 148 (1992), no. 2, 305–324. MR 1163738, DOI 10.1016/0021-8693(92)90196-S
- Curtis Greene, Proof of a conjecture on immanants of the Jacobi-Trudi matrix, Linear Algebra Appl. 171 (1992), 65–79. MR 1165445, DOI 10.1016/0024-3795(92)90250-E
- Nathan Jacobson, Lie algebras, Interscience Tracts in Pure and Applied Mathematics, No. 10, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962. MR 0143793
- Jens Carsten Jantzen, Moduln mit einem höchsten Gewicht, Lecture Notes in Mathematics, vol. 750, Springer, Berlin, 1979 (German). MR 552943
- Michio Jimbo, A $q$-analogue of $U({\mathfrak {g}}{\mathfrak {l}}(N+1))$, Hecke algebra, and the Yang-Baxter equation, Lett. Math. Phys. 11 (1986), no. 3, 247–252. MR 841713, DOI 10.1007/BF00400222
- V. F. R. Jones, Hecke algebra representations of braid groups and link polynomials, Ann. of Math. (2) 126 (1987), no. 2, 335–388. MR 908150, DOI 10.2307/1971403
- V. F. R. Jones, Index for subfactors, Invent. Math. 72 (1983), no. 1, 1–25. MR 696688, DOI 10.1007/BF01389127
- A. Joseph, Towards the Jantzen conjecture. I, II, Compositio Math. 40 (1980), no. 1, 35–67, 69–78. MR 558258
- David Kazhdan and George Lusztig, Representations of Coxeter groups and Hecke algebras, Invent. Math. 53 (1979), no. 2, 165–184. MR 560412, DOI 10.1007/BF01390031
- David Kazhdan and George Lusztig, Schubert varieties and Poincaré duality, Geometry of the Laplace operator (Proc. Sympos. Pure Math., Univ. Hawaii, Honolulu, Hawaii, 1979) Proc. Sympos. Pure Math., XXXVI, Amer. Math. Soc., Providence, R.I., 1980, pp. 185–203. MR 573434
- R. C. King and B. G. Wybourne, Characters of Hecke algebras $H_n(q)$ of type $A_{n-1}$, J. Phys. A 23 (1990), no. 23, L1193–L1197. MR 1086259
- Alain Lascoux and Marcel-Paul Schützenberger, Schubert polynomials and the Littlewood-Richardson rule, Lett. Math. Phys. 10 (1985), no. 2-3, 111–124. MR 815233, DOI 10.1007/BF00398147
- Elliott H. Lieb, Proofs of some conjectures on permanents, J. Math. Mech. 16 (1966), 127–134. MR 0202745, DOI 10.1512/iumj.1967.16.16008 D. E. Littlewood, The theory of group characters, 2nd ed., Oxford Univ. Press, London, 1950.
- I. G. Macdonald, Symmetric functions and Hall polynomials, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1979. MR 553598
- Arun Ram, A Frobenius formula for the characters of the Hecke algebras, Invent. Math. 106 (1991), no. 3, 461–488. MR 1134480, DOI 10.1007/BF01243921
- I. Schur, Über endliche Gruppen und Hermitesche Formen, Math. Z. 1 (1918), no. 2-3, 184–207 (German). MR 1544291, DOI 10.1007/BF01203611
- M.-P. Schützenberger, La correspondance de Robinson, Combinatoire et représentation du groupe symétrique (Actes Table Ronde CNRS, Univ. Louis-Pasteur Strasbourg, Strasbourg, 1976) Lecture Notes in Math., Vol. 579, Springer, Berlin, 1977, pp. 59–113 (French). MR 0498826 T. A. Springer, Quelques applications de la cohomologie d’intersection, Sém. Bourbaki 589 (1982).
- Richard P. Stanley, Log-concave and unimodal sequences in algebra, combinatorics, and geometry, Graph theory and its applications: East and West (Jinan, 1986) Ann. New York Acad. Sci., vol. 576, New York Acad. Sci., New York, 1989, pp. 500–535. MR 1110850, DOI 10.1111/j.1749-6632.1989.tb16434.x
- Richard P. Stanley and John R. Stembridge, On immanants of Jacobi-Trudi matrices and permutations with restricted position, J. Combin. Theory Ser. A 62 (1993), no. 2, 261–279. MR 1207737, DOI 10.1016/0097-3165(93)90048-D
- J. R. Stembridge, Some conjectures for immanants, Canad. J. Math. 44 (1992), no. 5, 1079–1099. MR 1186482, DOI 10.4153/CJM-1992-066-1
- John R. Stembridge, Eulerian numbers, tableaux, and the Betti numbers of a toric variety, Discrete Math. 99 (1992), no. 1-3, 307–320. MR 1158793, DOI 10.1016/0012-365X(92)90378-S
- John R. Stembridge, Immanants of totally positive matrices are nonnegative, Bull. London Math. Soc. 23 (1991), no. 5, 422–428. MR 1141010, DOI 10.1112/blms/23.5.422
- J. Van der Jeugt, An algorithm for characters of Hecke algebras $H_n(q)$ of type $A_{n-1}$, J. Phys. A 24 (1991), no. 15, 3719–3725. MR 1123644
- Hans Wenzl, Hecke algebras of type $A_n$ and subfactors, Invent. Math. 92 (1988), no. 2, 349–383. MR 936086, DOI 10.1007/BF01404457
Bibliographic Information
- © Copyright 1993 American Mathematical Society
- Journal: J. Amer. Math. Soc. 6 (1993), 569-595
- MSC: Primary 05E05; Secondary 14M15, 20C30, 20F55
- DOI: https://doi.org/10.1090/S0894-0347-1993-1186961-9
- MathSciNet review: 1186961