Equivalence classes in the Weyl groups of type B n
Thomas Pietraho
Bowdoin College Department of Mathematics Brunswick ME 04011 USA
DOI: 10.1007/s10801-007-0085-0
Abstract
We consider two families of equivalence classes in the Weyl groups of type B n which are suggested by the study of left cells in unequal parameter Iwahori-Hecke algebras. Both families are indexed by a non-negative integer r. It has been shown that the first family coincides with left cells corresponding to the equal parameter Iwahori-Hecke algebra when r=0; the equivalence classes in the second family agree with left cells corresponding to a special class of choices of unequal parameters when r is sufficiently large. Our main result shows that the two families of equivalence classes coincide, suggesting the structure of left cells for remaining choices of the Iwahori-Hecke algebra parameters.
Pages: 247–262
Keywords: keywords unequal parameter iwahori-Hecke algebra; domino tableaux; Robinson-Schensted algorithm
Full Text: PDF
References
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2. Bonnafé, C., Geck, M., Iancu, L., Lam, T.: On domino insertion and Kazhdan-Lusztig cells in type Bn. arXiv:math.RT/0609279
3. Carré, C., Leclerc, B.: Splitting the square of a Schur function into its symmetric and anti-symmetric parts. J. Algebr. Comb. 4, 201-231 (1995)
4. Garfinkle, D.: On the classification of primitive ideals for complex classical Lie algebras (I). Compos. Math. 75(2), 135-169 (1990)
5. Garfinkle, D.: On the classification of primitive ideals for complex classical Lie algebras (II). Compos. Math. 81(3), 307-336 (1992)
6. Garfinkle, D.: On the classification of primitive ideals for complex classical Lie algebras (III). Compos. Math. 88(2), 187-234 (1993) J Algebr Comb (2008) 27: 247-262
7. Gordon, I.G., Martino, M.: Calogero-Moser space, reduced rational Cherednik algebras and two-sided cells. arXiv:math.RT/0703153
8. Lusztig, G.: Left cells in Weyl groups. In: Lie Group Representations. Lecture Notes in Mathematics, vol. 1024, pp. 99-111 (1983)
9. Lusztig, G.: Hecke Algebras With Unequal Parameters. CRM Monograph Series, vol.
18. American Mathematical Society, Providence (2003)
10. McGovern, W.M.: Left cells and domino tableaux in classical Weyl groups. Compos. Math. 101(1), 77-98 (1996)
11. McGovern, W.M.: On the Spaltenstein-Steinberg map for classical Lie algebras. Commun. Algebra 27(6), 2979-2993 (1999)
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