Multi-parameter Cells of Finite Coxeter Groups
نویسندگان
چکیده
Cells of Coxeter groups are certain equivalence classes defined by the Kazhdan-Lusztig type basis of the associated Hecke algebra with a set of parameters. In this paper, we prove that, for finite Coxeter groups, cells arising from a multiparameter Hecke algebra are determined by those arising from a Hecke algebra with parameters which are powers of a single parameter.
منابع مشابه
Constructible Characters, Leading Coefficients and Left Cells for Finite Coxeter Groups with Unequal Parameters
Following Lusztig, we investigate constructible characters, leading coefficients and left cells for a finite Coxeter group W in the case of unequal parameters. We obtain explicit results for W of type F4, Bn and I2(m) (m even) which support Lusztig’s conjecture that known results about left cells in the equal parameter case should remain valid in the case of unequal parameters.
متن کاملGeneralized Nil-coxeter Algebras over Discrete Complex Reflection Groups
We define and study generalized nil-Coxeter algebras associated to Coxeter groups. Motivated by a question of Coxeter (1957), we construct the first examples of such finite-dimensional algebras that are not the ‘usual’ nil-Coxeter algebras: a novel 2-parameter type A family that we call NCA(n, d). We explore several combinatorial properties of NCA(n, d), including its Coxeter word basis, length...
متن کاملCharacterization of cyclically fully commutative elements in finite and affine Coxeter groups
An element of a Coxeter group is fully commutative if any two of its reduced decompositions are related by a series of transpositions of adjacent commuting generators. An element of a Coxeter group is cyclically fully commutative if any of its cyclic shifts remains fully commutative. These elements were studied by Boothby et al. In particular the authors precisely identified the Coxeter groups ...
متن کاملOn the Isomorphism Problem for Finitely Generated Coxeter Groups. I Basic Matching
The isomorphism problem for finitely generated Coxeter groups is the problem of deciding if two finite Coxeter matrices define isomorphic Coxeter groups. Coxeter [3] solved this problem for finite irreducible Coxeter groups. Recently there has been considerable interest and activity on the isomorphism problem for arbitrary finitely generated Coxeter groups. In this paper, we determine some stro...
متن کاملSupports of Irreducible Spherical Representations of Rational Cherednik Algebras of Finite Coxeter Groups
In this paper we determine the support of the irreducible spherical representation (i.e., the irreducible quotient of the polynomial representation) of the rational Cherednik algebra of a finite Coxeter group for any value of the parameter c. In particular, we determine for which values of c this representation is finite dimensional. This generalizes a result of Varagnolo and Vasserot, [VV], wh...
متن کامل