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Character values of Iwahori-Hecke algebras of type \(B\). (English) Zbl 0876.20011
Cabanes, Marc (ed.), Finite reductive groups: related structures and representations. Proceedings of an international conference, Luminy, France, October 1994. Boston, MA: Birkhäuser. Prog. Math. 141, 333-360 (1997).
Let \((W,S)\) be a Weyl group with generating set \(S\). The concept of the character table of a generic Iwahori-Hecke algebra \(H(W)\) of \(W\) was introduced by M. Geck and G. Pfeiffer [in Adv. Math. 102, No. 1, 79-94 (1993; Zbl 0816.20034)] as a square matrix which maps under specialization to the character table of the corresponding Weyl group \(W\). In this paper the author determines the character table for the Iwahori-Hecke algebra \(H(W)\) for \(W=B_n\). Some concepts of type \(A_n\) are generalized such as the Murnaghan-Nakayama formula and the Littlewood-Richardson rule. Computer programs such as GAP and CHEVIE are used in the calculation.
For the entire collection see [Zbl 0855.00019].

MSC:
20C33 Representations of finite groups of Lie type
20C34 Representations of sporadic groups
20C30 Representations of finite symmetric groups
Software:
CHEVIE
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