Susumu Ariki

Cyclotomic Nazarov-Wenzl algebras

Nazarov [Naz96] introduced an infinite dimensional algebra, which he called the affine Wenzl algebra , in his study of the Brauer algebras. In this paper we study certain “cyclotomic quotients” of these algebras. We construct the irreducible representations of these algebras in the generic case and use this to show that these algebras are free of rank r n ( 2n −1)!! (when Ω is u-admissible). We next show that these algebras are cellular and give a labelling for the simple modules of the cyclotomic Nazarov-Wenzl algebras over an arbitrary field. In particular, this gives a construction of all of the finite dimensional irreducible modules of the affine Wenzl algebra.

The representation type of Hecke algebras of type B

Abstract This paper determines the representation type of the Iwahori–Hecke algebras of type B when q ≠±1. In particular, we show that a single parameter non-semisimple Iwahori–Hecke algebra of type B has finite representation type if and only if q is a simple root of the Poincare polynomial, confirming a conjecture of Unos (J. Algebra 149 (1992) 287).

Hecke Algebras of Classical Type and Their Representation Type

The purpose of this article is to determine the representation type for all of the Hecke algebras of classical type. To do this, we combine methods from our previous work, which is used to obtain information on their Gabriel quivers, and recent advances in the theory of finite-dimensional algebras. The principal computation is for Hecke algebras of type B with two parameters. Then, we show that the representation type of Hecke algebras is governed by their Poincare polynomials.

Factorization of the canonical bases for higher-level Fock spaces

The level l Fock space admits canonical bases G_e and G_\infty. They correspond to U_{v}(hat{sl}_{e}) and U_{v}(sl_{\infty})-module structures. We establish that the transition matrices relating these two bases are unitriangular with coefficients in N[v]. Restriction to the highest weight modules generated by the empty l-partition then gives a natural quantization of a theorem by Geck and Rouquier on the factorization of decomposition matrices which are associated to Ariki-Koike algebras.

Dipper–James–Murphy’s Conjecture for Hecke Algebras of Type Bn

We prove a conjecture by Dipper, James, and Murphy that a bipartition is restricted if and only if it is Kleshchev. Hence, the restricted bipartitions naturally label the crystal graphs of level 2 irreducible integrable \({\mathcal{U}}_{v}(\widehat{{\mathfrak{s}\mathfrak{l}}}_{e})\)-modules and the simple modules of Hecke algebras of type B n in the non semisimple case.

Algebraic Groups and Quantum Groups

Let g be a complex simple Lie algebra, f a nilpotent element of g. We show that (1) the center of the W -algebra Wcri(g, f) associated (g, f) at the critical level coincides with the Feigin-Frenkel center of ĝ, (2) the centerless quotient Wχ(g, f) of Wcri(g, f) corresponding to an Lg-oper χ on the disc is simple, and (3) the simple quotient Wχ(g, f) is a quantization of the jet scheme of the intersection of the Slodowy slice at f with the nilpotent cone of g.

ON COMPONENTS OF STABLE AUSLANDER–REITEN QUIVERS THAT CONTAIN HELLER LATTICES: THE CASE OF TRUNCATED POLYNOMIAL RINGS

Let

Hecke algebras of classical type and their representation type (proc. london math. soc. (3) 91 (2005) 355-413)

A

Representations of Quantum Algebras and Combinatorics of Young Tableaux

be a truncated polynomial ring over a complete discrete valuation ring

Proof of the modular branching rule for cyclotomic Hecke algebras

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