Related papers: On two group functors extending Schur multipliers

Given a group $G$ and an integer $n\geq2$ we construct a new group $\tilde{{\cal K}}(G,n)$. Although this construction naturally occurs in the context of finding new invariants for complex algebraic surfaces, it is related to the theory of…

The Schur function expansion of Sato-Segal-Wilson KP tau-functions is reviewed. The case of tau-functions related to algebraic curves of arbitrary genus is studied in detail. Explicit expressions for the Pl\"ucker coordinate coefficients…

The theory of Schur functors provides a powerful and elegant approach to the representation theory of GL_n - at least to the so-called polynomial representations - especially to questions about how the theory varies with n. We develop…

We develop a theory of two-parameter quantum polynomial functors. Similar to how (strict) polynomial functors give a new interpretation of polynomial representations of the general linear groups $\operatorname{GL}_n$, the two-parameter…

Let $G$ be a central product of two groups $H$ and $K$. We study second cohomology group of $G$, having coefficients in a divisible abelian group $D$ with trivial $G$-action, in terms of the second cohomology groups of certain quotients of…

Let $k$ be a commutative $\mathbb{Q}$-algebra. We study families of functors between categories of finitely generated $R$-modules which are defined for all commutative $k$-algebras $R$ simultaneously and are compatible with base changes.…

We study the class $\mathcal C$ of symmetric functions whose coefficients in the Schur basis can be described by generating functions for sets of tableaux with fixed shape. Included in this class are the Hall-Littlewood polynomials,…

We prove that each exponential functor on the category of finite-dimensional complex inner product spaces and isomorphisms gives rise to an equivariant higher (ie. non-classical) twist of $K$-theory over $G=SU(n)$. This twist is represented…

In this article we study support $\tau$-tilting modules, semibricks and more over blocks of group algebras. Let $k$ be an algebraically closed field of characteristic $p>0$, $\tilde{G}$ a finite group and $G$ a normal subgroup of…

We give geometric descriptions of the category C_k(n,d) of rational polynomial representations of GL_n over a field k of degree d for d less than or equal to n, the Schur functor and Schur-Weyl duality. The descriptions and proofs use a…

Let $p$ be an odd prime. We describe a method to compute the Schur multiplier of finite $p$-groups $G$ of nilpotency class $2$ such that $G/[G,G]$ is isomorphic to direct product of copies of $\mathbb{Z}_{p^s}$ for $s \in \mathbb{N}$,…

From [Problem 1729, Groups of prime power order, Vol. 3], Berkovich et al. asked to obtain the Schur multiplier and the representation of a group $G$, when $G$ is a special $p$-group minimally generated by $d$ elements and…

Let $K:k$ be a field extension and let $\Lambda$ be a finite-dimensional $k$-algebra. We investigate the relationship between $\Lambda$ and $\Lambda_K = \Lambda \otimes_k K$ with particular emphasis on various aspects of $\tau$-tilting…

The affine Schur algebra $\widetilde{S}(n,r)$ (of type A) over a field $K$ is defined to be the endomorphism algebra of the tensor space over the extended affine Weyl group of type $A_{r-1}$. By the affine Schur-Weyl duality it is…

We study \tau-functions of the KP hierarchy in terms of abelian group actions on finite dimensional Grassmannians, viewed as subquotients of the Hilbert space Grassmannians of Sato, Segal and Wilson. A determinantal formula of Gekhtman and…

We associate to each unital $C^*$-algebra $A$ a geometric object---a diagram of topological spaces representing quotient spaces of the noncommutative space underlying $A$---meant to serve the role of a generalized Gel'fand spectrum. After…

Given a symmetry $\tau$ of a closed Riemann surface $S$, there exists an extended Kleinian group $K$, whose orientation-preserving half is a Schottky group $\Gamma$ uniformizing $S$, such that $K/\Gamma$ induces $\langle \tau \rangle$; the…

We describe an algorithm for computing successive quotients of the Schur multiplier $M(G)$ for a group $G$ given by an invariant finite $L$-presentation. As application, we investigate the Schur multipliers of various self-similar groups…

Let $K$ be a finite group and let $G$ be a finite group acting on $K$ by automorphisms. In this paper we study two different but intimately related subjects: on the one side we classify all possible multiplicative and associative structures…

The main aim of the article is to find the Schur multiplier and the Lie exterior square of some finite multiplicative Lie algebras. For a non abelian simple group $K$ with trivial Schur multiplier, we see that the Schur multiplier of…