Related papers: Gelfand models and Robinson-Schensted corresponden…
In [F. Caselli, Involutory reflection groups and their models, J. Algebra 24 (2010), 370--393] it is constructed a uniform Gelfand model for all non-exceptional irreducible complex reflection groups which are involutory. This model can be…
A finite subgroup of $GL(n,\mathbb C)$ is involutory if the sum of the dimensions of its irreducible complex representations is given by the number of absolute involutions in the group. A uniform combinatorial model is constructed for all…
A Gelfand model for a semisimple algebra A over C is a complex linear representation that contains each irreducible representation of A with multiplicity exactly one. We give a method of constructing these models that works uniformly for a…
This paper provides results on the modular representation theory of the supergroup $GL(m|n).$ Working over a field of arbitrary characteristic, we prove that the explicit combinatorics of certain crystal graphs describe the representation…
We prove that a finite complex reflection group has a generalized involution model, as defined by Bump and Ginzburg, if and only if each of its irreducible factors is either $G(r,p,n)$ with $\gcd(p,n)=1$; $G(r,p,2)$ with $r/p$ odd; or…
A Gelfand model for an algebra is a module given by a direct sum of irreducible submodules, with every isomorphism class of irreducible modules represented exactly once. We introduce the notion of a perfect model for a finite Coxeter group,…
The Gelfand representation of $\mathcal{S}_n$ is the multiplicity-free direct sum of the irreducible representations of $\mathcal{S}_n$. In this paper, we use a result of Adin, Postnikov, and Roichman to find a recursive generating function…
The main result of this paper is a generalization of the theorem of Chevalley-Shephard-Todd to the rings of invariants of pseudoreflection groups over Dedekind domains. In the special case of a principal ideal domain in which the group…
We classify the irreducible representations of smooth, connected affine algebraic groups over a field, by tackling the case of pseudo-reductive groups. We reduce the problem of calculating the dimension for pseudo-split pseudo-reductive…
We provide a classification and explicit bases of tableaux of all irreducible generic Gelfand-Tsetlin modules for the Lie algebra $\mathfrak{gl}(n)$.
Combinatorial aspects of multivariate diagonal invariants of the symmetric group are studied. As a consequence it is proved the existence of a multivariate extension of the classical Robinson-Schensted correspondence. Further byproduct are…
A Gelfand model for a finite group $G$ is a complex linear representation of $G$ that contains each of its irreducible representations with multiplicity one. For a finite group $G$ with a faithful representation $V$, one constructs a…
We provide a classification and an explicit realization of all irreducible Gelfand-Tsetlin modules of the complex Lie algebra sl(3). The realization of these modules uses regular and derivative Gelfand-Tsetlin tableaux. In particular, we…
In this note, we study irreducible unitary representations of special linear groups of lower ranks, in terms of the matrix models of Gelfand-Naimark and Gelfand-Graev. Review of existing literature is provided. We also add some new…
We introduce the class of projective reflection groups which includes all complex reflection groups. We show that several aspects involving the combinatorics and the representation theory of all non exceptional irreducible complex…
Ehrenborg and Jung recently related the order complex for the lattice of d-divisible partitions with the simplicial complex of pointed ordered set partitions via a homotopy equivalence. The latter has top homology naturally identified as a…
In 1970, Gelfand posed the problem of classifying the indecomposable objects in a representation category equivalent to the principal block of Harish-Chandra modules for $\mathsf{SL}_2(\mathbb{R})$; explicit solutions were obtained by…
We prove a conjecture for the irreducibility of singular Gelfand-Tsetlin modules. We describe explicitly the irreducible subquotients of certain classes of singular Gelfand-Tsetlin modules.
There are known to be integrable Sutherland models associated to every real root system -- or, which is almost equivalent, to every real reflection group. Real reflection groups are special cases of complex reflection groups. In this paper…
We obtain a complete classification of the continuous unitary representations of oligomorphic permutation groups (those include the infinite permutation group $S_\infty$, the automorphism group of the countable dense linear order, the…