Caenepeel, Frederik Oystaeyen, Fred Van
Published in
Algebras and Representation Theory

We continue the study of glider representations of finite groups G with given structure chain of subgroups e ⊂ G1 ⊂… ⊂ Gd = G. We give a characterization of irreducible gliders of essential length e ≤ d which in the case of p-groups allows to prove some results about classical representation theory. The paper also contains an introduction to genera...

Positselski, Leonid
Published in
Algebras and Representation Theory

We present the definition of a dedualizing complex of bicomodules over a pair of cocoherent coassociative coalgebras C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\ma...

Lawton, Sean Sikora, Adam S.
Published in
Algebras and Representation Theory

Let G be a connected reductive affine algebraic group. In this short note we define the variety of G-characters of a finitely generated group Γ and show that the quotient of the G-character variety of Γ by the action of the trace preserving outer automorphisms of G normalizes the variety of G-characters when Γ is a free group, free abelian group, o...

Chaio, Claudia Le Meur, Patrick Trepode, Sonia
Published in
Algebras and Representation Theory

The module category of any artin algebra is filtered by the powers of its radical, thus defining an associated graded category. As an extension of the degree of irreducible morphisms, this text introduces the degree of morphisms in the module category. When the ground ring is a perfect field, and the given morphism behaves nicely with respect to co...

Ariki, S. Kase, R. Miyamoto, K. Wada, K.
Published in
Algebras and Representation Theory

We classify Morita equivalence classes of indecomposable self-injective cellular algebras which have polynomial growth representation type, assuming that the characteristic of the base field is different from two. This assumption on the characteristic is for the cellularity to be a Morita invariant property.

Guo, Jin Yun Luo, Deren
Published in
Algebras and Representation Theory

In this paper we study a class of algebras having n-dimensional pyramid shaped quiver with n-cubic cells, which we called n-cubic pyramid algebras. This class of algebras includes the quadratic dual of the basic n-Auslander absolutely n-complete algebras introduced by Iyama. We show that the projective resolutions of the simples of n-cubic pyramid ...

Ovsienko, Valentin Tabachnikov, Serge
Published in
Algebras and Representation Theory

We investigate a general method that allows one to construct new integer sequences extending existing ones. We apply this method to the classic Somos-4 and Somos-5, and the Gale-Robinson sequences, as well as to more general class of sequences introduced by Fordy and Marsh, and produce a great number of new sequences. The method is based on the not...

Kobayashi, Toshiyuki Nasrin, Salma
Published in
Algebras and Representation Theory

Consider the restriction of an irreducible unitary representation π of a Lie group G to its subgroup H. Kirillov’s revolutionary idea on the orbit method suggests that the multiplicity of an irreducible H-module ν occurring in the restriction π|H could be read from the coadjoint action of H on OG∩pr−1(OH)\documentclass[12pt]{minimal} \usepackage{am...

Bouarroudj, Sofiane Krutov, Andrey Leites, Dimitry Shchepochkina, Irina
Published in
Algebras and Representation Theory

We review the list of non-degenerate invariant (super)symmetric bilinear forms (briefly: NIS) on the following simple (relatives of) Lie (super)algebras: (a) with symmetrizable Cartan matrix of any growth, (b) with non-symmetrizable Cartan matrix of polynomial growth, (c) Lie (super)algebras of vector fields with polynomial coefficients, (d) string...

Ginzburg, Victor Rozenblyum, Nick
Published in
Algebras and Representation Theory

Let BunG be the moduli space of G-bundles on a smooth complex projective curve. Motivated by a study of boundary conditions in mirror symmetry, Gaiotto (2016) associated to any symplectic representation of G a Lagrangian subvariety of T∗BunG. We give a simple interpretation of (a generalization of) Gaiotto’s construction in terms of derived symplec...