Related papers: A numerical invariant for linear representations o…

We consider the representation dimension, for fixed $n\geq2$, of ordinary and quantised Schur algebras $S(n,r)$ over a field $k$. For $k$ of positive characteristic $p$ we give a lower bound valid for all $p$. We also give an upper bound in…

We study the essential dimension of representations of a fixed quiver with given dimension vector. We also consider the question of when the genericity property holds, i.e., when essential dimension and generic essential dimension agree. We…

We propose an algorithm for computing bases and dimensions of spaces of invariants of Weil representations of $\mathrm{SL}_2(\mathbb{Z})$ associated to finite quadratic modules. We prove that these spaces are defined over $\mathbb{Z}$, and…

In this article, we study the Schur mutiplier of the discrete as well as the finite Heisenberg groups and their t-variants. We describe the representation groups of these Heisenberg groups and through these give a construction of their…

The integral formulae pertaining to the unitary group $\mathsf{U}(d)$ have been comprehensively reviewed, yielding fresh results and innovative proofs. Central to the derivation of these formulae lies the employment of Schur-Weyl duality, a…

We study the essential dimension of a finite group G over a field K. A generalization of the central extension theorem of Buhler and Reichstein (Compositio Math. 106 (1997) 159-179, Theorem 5.3) is obtained. We also get lower bounds of…

One of the important open problems in the theory of central simple algebras is to compute the essential dimension of $\operatorname{GL}_n/\mu_m$, i.e., the essential dimension of a generic division algebra of degree $n$ and exponent…

We extend the family of classical Schur algebras in type A, which determine the polynomial representation theory of general linear groups over an infinite field, to a larger family, the rational Schur algebras, which determine the rational…

With this work we initiate a study of the representations of a unipotent group over a field of characteristic zero from the modular point of view. Let $G$ be such a group. The stack of all representations of a fixed finite dimension $n$ is…

Let X be the variety obtained by the Weil transfer with respect to a quadratic separable field extension of a generalized Severi-Brauer variety. We study (and, in some cases, determine) the canonical dimension, incompressibility, and…

We give criteria for finite dimensionality or infinite dimensionality of the polynomial centralizer of the Lie algebra of a linear Lie group, in terms of invariants and relative invariants of the group. In the finite dimensional scenario…

To a finite quadratic module, that is, a finite abelian group D together with a non-singular quadratic form Q:D --> Q/Z, it is possible to associate a representation of either the modular group, SL(2,Z), or its metaplectic cover, Mp(2,Z),…

Based on recent successes concerning permutation resolutions of representations by Balmer and Gallauer we define a new invariant of finite groups: the p-permutation dimension. We define this analogously to the global dimension of a ring by…

We prove that an abstract (possibly infinite dimensional) complex irreducible representation of a discrete supersolvable group is monomial if and only if it has finite weight. We also prove a general result that implies converse of Schur's…

We investigate the Schr\"odinger representations of certain infinite-dimensional Heisenberg groups, using their corresponding Wigner transforms.

We extend the classical Schur-Weyl duality between representations of the groups $SL(n,\C)$ and $\sN$ to the case of $SL(n,\C)$ and the infinite symmetric group $\sinf$. Our construction is based on a "dynamic," or inductive, scheme of…

We extend Auslander and Buchsbaum's Euler characteristic from the category of finitely generated modules of finite projective dimension to the category of modules of finite G-dimension using Avramov and Martsinkovsky's notion of relative…

We consider the dimensions of finite type of representations of a partially ordered set, i.e. such that there is only finitely many isomorphism classes of representations of this dimension. We give a criterion for a dimension to be of…

The main result describes the Brauer-Nesbitt reduction of unipotent representations of a finite group of Lie type, expressing it as an explicit linear combination of the restriction of Weyl modules from the algebraic group to the group of…

To each irreducible infinite dimensional representation $(\pi,\cH)$ of a $C^*$-algebra $\cA$, we associate a collection of irreducible norm-continuous unitary representations $\pi_{\lambda}^\cA$ of its unitary group $\U(\cA)$, whose…