We show that, over an arbitrary field, q-rook monoid algebras are iterated inflations of Iwahori-Hecke algebras, and, in particular, are cellular. Furthermore we give an algebra decomposition which shows a q-rook monoid algebra is Morita equivalent to a direct sum of Iwahori-Hecke algebras. We state some of the consequences for the representation theory of q-rook monoid algebras.

We derive a parameterization of simple modules for the cyclotomic Hecke algebras of type G(r, p, n) over field of any characteristic coprime to p. We give explicit formulas for the number of simple modules over these cyclotomic Hecke algebras.

We prove that any Hecke eigenclass in the mod p cohomology of a congruence subgroup of GL(1,Z) or GL(2,Z) has attached to it a mod p Galois representation such that the characteristic polynomial of a Frobenius element at a prime l equals the Hecke polynomial at l.

Let R be a field of any characteristic and A a principal ideal domain. We make a conjecture that asserts that any Hecke operator T acts punctually on any Hecke eigenclass in the stable homology with trivial coefficients R of a principal congruence subgroup Γ in GL(n, A), i.e. as multiplication by the number of single cosets contained in T . In the case where A = Z, this conjecture implies that ...

For any finite Coxeter group W , we introduce two new objects: its cutting poset and its biHecke monoid. The cutting poset, constructed using a generalization of the notion of blocks in permutation matrices, almost forms a lattice on W . The construction of the biHecke monoid relies on the usual combinatorial model for the 0-Hecke algebra H0(W ), that is, for the symmetric group, the algebra (o...

This paper introduces the notion of calibrated representations for aane Hecke algebras and classiies and constructs all nite dimensional irreducible calibrated representations. The main results are that (1) irreducible calibrated representations are indexed by placed skew shapes, (2) the dimension of an irreducible calibrated representation is the number of standard Young tableaux corresponding...

This paper introduces the notion of calibrated representations for affine Hecke algebras and classifies and constructs all finite dimensional irreducible calibrated representations. The main results are that (1) irreducible calibrated representations are indexed by placed skew shapes, (2) the dimension of an irreducible calibrated representation is the number of standard Young tableaux correspo...

The cyclotomic Hecke algebras were introduced by Ariki and Koike [2,4] and Broué and Malle [7]. It is conjectured [7] that these algebras play a rôle in the representation theory of reductive groups similar to (but more complicated than) that played by the Iwahori–Hecke algebras (see, for example, [8]). In particular, it should be possible to use these algebras to compute the degrees (and more ...

We present a formalization using data uniquely de ned at the level of the Weyl group of the construction and combinatorial properties of unipotent character shea ves and unipotent characters for reductive algebraic groups over an algebraic closure of a nite eld This formalization extends to the case where the Weyl group is re placed by a complex re ection group and in many cases we get families...

We investigate the connection between integral weight and half-integral weight modular forms. Building on results of Ueda 14], we obtain structure theorems for spaces of half-integral weight cusp forms S k=2 (4N;) where k and N are odd nonnegative integers with k 3, and is an even quadratic Dirichlet character modulo 4N. We give complete results in the case where N is a power of a single prime,...