Knuth relations for the hyperoctahedral groups
Thomas Pietraho
Bowdoin College Brunswick ME 04011 USA
DOI: 10.1007/s10801-008-0148-x
Abstract
C. Bonnafé, M. Geck, L. Iancu, and T. Lam have conjectured a description of Kazhdan-Lusztig cells in unequal parameter Hecke algebras of type B which is based on domino tableaux of arbitrary rank. In the integer case, this generalizes the work of D. Garfinkle. We adapt her methods and construct a family of operators which generate the equivalence classes on pairs of arbitrary rank domino tableaux described in the above conjecture.
Pages: 509–535
Keywords: keywords unequal parameter iwahori-Hecke algebra; domino tableaux; Robinson-Schensted algorithm
Full Text: PDF
References
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3. Bonnafé, C., Geck, M., Iancu, L., Lam, T.: On domino insertion and Kazhdan-Lusztig cells in type Bn. In: Progress in Math. (Lusztig Birthday Volume). Birkhauser, Boston (to appear)
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5. Garfinkle, D.: On the classification of primitive ideals for complex classical Lie algebras (II). Compositio Math. 81(3), 307-336 (1992)
6. Garfinkle, D.: On the classification of primitive ideals for complex classical Lie algebras (III). Compositio Math. 88(2), 187-234 (1993)
7. Geck, M.: Computing Kazhdan-Lusztig cells for unequal parameters. J. Algebra 281(1), 342-365 (2004)
8. Gordon, I.G., Martino, M.: Calogero-Moser Space, reduced rational Cherednik algebras and twosided cells. arXiv
9. Hopkins, B.: Domino tableaux and single-valued wall-crossing operators. Ph.D. dissertation, University of Washington (1997)
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19. Taskin, M.: Plactic relations for r -domino tableaux. arXiv:20. van Leeuwen, M.A.A.: The Robinson-Schensted and Schutzenberger algorithms, an elementary approach. Electron. J. Comb. 3(2) (1996)
21. Vogan, D.: A generalized τ-invariant for the primitive spectrum of a semisimple Lie algebra. Math.