Schur elements for the Ariki-Koike algebra and applications
Maria Chlouveraki
and Nicolas Jacon
DOI: 10.1007/s10801-011-0314-4
Abstract
We study the Schur elements associated to the simple modules of the Ariki-Koike algebra. We first give a cancellation-free formula for them so that their factors can be easily read and programmed. We then study direct applications of this result. We also complete the determination of the canonical basic sets for cyclotomic Hecke algebras of type G( l, p, n) in characteristic 0.
Pages: 291–311
Keywords: keywords Hecke algebras; complex reflection groups; Schur elements; blocks; basic sets
Full Text: PDF
References
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2. Ariki, S.: Representations of Quantum Algebras and Combinatorics of Young Tableaux. University Lecture Series, vol.
26. American Mathematical Society, Providence (2002)
3. Ariki, S., Koike, K.: A Hecke algebra of (Z/rZ) Sn and construction of its irreducible representations. Adv. Math. 106, 216-243 (1994)
4. Bremke, K., Malle, G.: Reduced words and a length function for G(e, 1, n). Indag. Math. 8, 453-469 (1997)
5. Chlouveraki, M.: Blocks and Families For Cyclotomic Hecke Algebras. LNM, vol.
1981. Springer, Berlin (2009)
6. Chlouveraki, M., Jacon, N.: Schur elements and Basic sets for Cyclotomic Hecke algebras. J. Algebra Appl. (to appear)
7. Chlouveraki, M., Gordon, I., Griffeth, S.: Cell modules and canonical basic sets for Hecke algebras from Cherednik algebras. Contemp. Math. (to appear).
8. Dipper, R., Mathas, A.: Morita equivalences of Ariki-Koike algebras. Math. Z. 240(3), 579-610 (2002)
9. Dunkl, C., Griffeth, S.: Generalized Jack polynomials and the representation theory of rational Cherednik algebras.
10. Fayers, M.: Weights of multipartitions and representations of Ariki-Koike algebras. II. Canonical bases. J. Algebra 319(7), 2963-2978 (2008)
11. Geck, M., Jacon, N.: Irreducible Representations of Hecke Algebras at Roots of Unity. Algebras and Applications, vol.
15. Springer, London (2011)
12. Geck, M., Pfeiffer, G.: Characters of Finite Coxeter Groups and Iwahori-Hecke Algebras. London Mathematical Society Monographs. New Series, vol.
21. Oxford University Press, New York (2000)
13. Geck, M., Iancu, L., Malle, G.: Weights of Markov traces and generic degrees. Indag. Math. 11, 379- 397 (2000)
14. Genet, G., Jacon, N.: Modular representations of cyclotomic Hecke algebras of type G(r, p, n). Int.
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