Related papers: Set families and Foulkes modules

We classify all homomorphisms between Weyl modules for SL_3(k) when k is an algebraically closed field of characteristic at least three, and show that the Hom-spaces are all at most one-dimensional. As a corollary we obtain all…

We analyze cyclic cell modules over walled Brauer algebra in terms of a certain normal form. The latter allows us to decompose the algebra into the generating set and annihilator ideal of a certain cyclic vector. In addition, we show that…

In this note we are interested in labelling the irreducible representations of non-semisimple specialisations of Hecke algebras of complex reflection groups. We will use category O for the rational Cherednik algebra and the KZ functor…

We obtain a new family of relations satisfied by the partition function. In contrast with most partition relations, these involve non-trivial roots of unity. We present two proofs, one using the fact that the discriminant modular form is a…

This paper describes the module categories for a family of generic Hecke algebras that specialize to the complex reflection groups G(r,1,n) and to the certain endomorphism rings of permutation characters of finite general linear groups. In…

Orthogonal sets of idempotents are used to design sets of unitary matrices, known as constellations, such that the modulus of the determinant of the difference of any two distinct elements is greater than $0$. It is shown that unitary…

We characterize the smallest finite spaces with the same homotopy groups of the spheres. Similarly, we describe the minimal finite models of any finite graph. We also develop new combinatorial techniques based on finite spaces to study…

We study new families of curves that are suitable for efficiently parametrizing their moduli spaces. We explicitly construct such families for smooth plane quartics in order to determine unique representatives for the isomorphism classes of…

We consider all Bott-Samelson varieties ${\rm BS}(s)$ for a fixed connected semisimple complex algebraic group with maximal torus $T$ as the class of objects of some category. The class of morphisms of this category is an extension of the…

The Weil representation of the symplectic group associated to a finite abelian group of odd order is shown to have a multiplicity-free decomposition. When the abelian group is p-primary, the irreducible representations occurring in the Weil…

We introduce a family of sequence transformations, defined via partial Bell polynomials, that may be used for a systematic study of a wide variety of problems in enumerative combinatorics. This family includes some of the transformations…

We show that the cobordism class of a polarization of Hodge module defines a natural transformation from the Grothendieck group of Hodge modules to the cobordism group of self-dual bounded complexes with real coefficients and constructible…

We introduce a class of polynomials that we call fused Specht polynomials and use them to characterize irreducible representations of the fused Hecke algebra with parameter $q=-1$ in the space of polynomials. We apply the fused Specht…

We study the decomposability of Specht modules labelled by bihooks, bipartitions with a hook in each component, for the Iwahori--Hecke algebra of type $B$. In all characteristics, we determine a large family of decomposable Specht modules,…

We study homomorphisms of Hecke monoids, notably parabolic homomorphisms, which map parabolic elements to parabolic elements, and injective ones. The importance of the first class stems from the fact that parabolic elements form a rather…

We introduce and study families of finite index subgroups of the modular group that generalize the congruence subgroups. Such groups, termed $\phi$-congruence subgroups, are obtained by reducing homomorphisms $\phi$ from the modular group…

We introduce a generalization of degenerate affine Hecke algebra, called wreath Hecke algebra, associated to an arbitrary finite group G. The simple modules of the wreath Hecke algebra and of its associated cyclotomic algebras are…

The following thesis contains results on the combinatorial representation theory of the finite Hecke algebra $H_n(q)$. In Chapter 2 simple combinatorial descriptions are given which determine when a Specht module corresponding to a…

Let $\mathbb{M}$ be the Monster finite simple group. We give an interpretation of certain discrete symmetries of a family of heterotic string compactifications to $1 + 1$ dimensions in terms of discrete symmetries of the Monster Lie algebra…

We extend the Howlett-Isaacs theorem on the solvability of groups of central type taking into account actions by automorphisms. Then we study certain induced characters whose constituents have all the same degree.