Left Cells and Constructible Representations
نویسنده
چکیده
We consider the partition of a finite Coxeter group W into left cells with respect to a weight function L. In the equal parameter case, Lusztig has shown that the representations carried by the left cells are precisely the so-called constructible ones. We show that this holds for general L, if the conjectural properties (P1)–(P15) in Lusztig’s book on Hecke algebras with unequal parameters hold for W,L. Our proofs use the idea (Gyoja, Rouquier) that left cell representations are projective in the sense of modular representation theory. This also gives partly new proofs for Lusztig’s result in the equal parameter case.
منابع مشابه
LEFT CELLS IN TYPE Bn WITH UNEQUAL PARAMETERS
Kazhdan and Lusztig have shown that the partition of the symmetric group Sn into left cells is given by the Robinson–Schensted correspondence. The aim of this paper is to provide a similar description of the left cells in type Bn for a special class of choices of unequal parameters. This is based on a generalization of the Robinson–Schensted correspondence in type Bn. We provide an explicit des...
متن کاملConstructible 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 کاملErratum to “left Cells and Constructible Representations”
Thomas Pietraho pointed out a problem in the proof of one of the main results in “Left cells and constructible representations”, Represent. Theory 9 (2005), 385–416. The purpose of this note is to correct this problem. The author is grateful to Thomas Pietraho for pointing out a problem in the proof of [2, Theorem 3.7(b)]. That problem is caused by a reference to [2, Remark 2.4], which in turn ...
متن کاملConstructible Authentic Representations: Designing Video Games that Enable Players to Utilize Knowledge Developed In-Game to Reason About Science
While video games have become a source of excitement for educational designers, creating informal game experiences that players can draw on when thinking and reasoning in non-game contexts has proved challenging. In this paper we present a design principle for creating educational video games that enables players to draw on knowledge resources gained in-game to reason about non-game phenomena. ...
متن کاملTHE LEFT REGULAR REPRESENTATION OF A COMMUTATIVE SEPARATIVE SEMIGROUP
In this paper, a commutative semigroup will be written as a disjoint union of its cancellative subsemigroups. Based on this fact we will define the left regular representation of a commutative separative semigroup and show that this representation is faithful. Finally concrete examples of commutative separative semigroups, their decompositions and their left regular representations are given.
متن کامل