Related papers: Hibi algebras and representation theory
We present an application of Hodge theory towards the study of irreducible unitary representations of reductive Lie groups. We describe a conjecture about such representations and discuss some progress towards its proof.
We study the relation between algebraic structures and Graph Theory. We have defined five different weighted digraphs associated to a finite dimensional algebra over a field in order to tackle important properties of the associated…
In this paper we study the representation theory for certain ``half lattice vertex algebras.'' In particular we construct a large class of irreducible modules for these vertex algebras. We also discuss how the representation theory of these…
Associated to the classical Weyl groups, we introduce the notion of degenerate spin affine Hecke algebras and affine Hecke-Clifford algebras. For these algebras, we establish the PBW properties, formulate the intertwiners, and describe the…
We construct representation theory of Lie algebras with filtrations. In this framework a classification of irreducible representations is obtained and spectra of some reducible representations are found.
We discuss the Hodge theory of algebraic non-commutative spaces and analyze how this theory interacts with the Calabi-Yau condition and with mirror symmetry. We develop an abstract theory of non-commutative Hodge structures, investigate…
We start with definitions of the general notions of the theory of $\Bbb Z_{2}$-graded algebras. Then we consider theory of inductive families of $\Bbb Z_{2}$-graded semisimple finite-dimensional algebras and its representations in the…
In this paper, we introduce a representation theory of Hom-Lie conformal superalgebras and discuss the cases of adjoint representations. Furthermore, we develop cohomology theory of Hom-Lie conformal superalgebras and discuss some…
The supercharacter theory of algebra groups gave us a representation theoretic realization of the Hopf algebra of symmetric functions in noncommuting variables. The underlying representation theoretic framework comes equipped with two…
Let W be a finite Coxeter group. We define its Hecke-group algebra by gluing together appropriately its group algebra and its 0-Hecke algebra. We describe in detail this algebra (dimension, several bases, conjectural presentation,…
Hodge representations were introduced by Green-Griffiths-Kerr to classify the Hodge groups of polarized Hodge structures, and the corresponding Mumford-Tate subdomains of a period domain. The purpose of this article is to provide an…
We study the structure of a family of algebras which encodes a generalization of the Pieri Rule for the complex orthogonal group. In particular, we show that each of these algebras has a standard monomial basis and has a flat deformation to…
This tutorial is intended to give an accessible introduction to Hopf algebras. The mathematical context is that of representation theory, and we also illustrate the structures with examples taken from combinatorics and quantum physics,…
This is a survey paper about affine Hecke algebras. We start from scratch and discuss some algebraic aspects of their representation theory, referring to the literature for proofs. We aim in particular at the classification of irreducible…
Bialgebras and Hopf (bi)modules are typical algebraic structures with several interacting operations. Their structural and homological study is therefore quite involved. We develop the machinery of braided systems, tailored for handling…
We introduce and study some affine Hecke algebras of type ADE, generalising the affine Hecke algebras of GL. We construct irreducible calibrated representations and describe the calibrated spectrum. This is done in terms of new families of…
With a basic knowledge of cohomology theory, the background necessary to understand Hodge theory and polarization, Deligne's Mixed Hodge Structure on cohomology of complex algebraic varieties is described.
We discuss algebraic and representation theoretic structures in braided tensor categories C which obey certain finiteness conditions. Much interesting structure of such a category is encoded in a Hopf algebra H in C. In particular, the Hopf…
In order to understand the structure of the cohomologies involved in the study of projectively equivariant quantizations, we introduce a notion of affine representation of a Lie algebra.We show how it is related to linear representations…
We apply the effective integration theory of Lie-graph algebras, developed recently by the authors, to the deformation and homotopy theories of types of bialgebras, that is structures controlled by a properad, like associative bialgebras,…