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Lectures on tensor categories and modular functors

- B. Bakalov, A. Kirillov
- Mathematics
- 20 November 2000

Introduction Braided tensor categories Ribbon categories Modular tensor categories 3-dimensional topological quantum field theory Modular functor Moduli spaces and complex modular functor… Expand

Braided Tensor Categories and Extensions of Vertex Operator Algebras

- Yi-Zhi Huang, A. Kirillov, J. Lepowsky
- Mathematics
- 13 June 2014

Let V be a vertex operator algebra satisfying suitable conditions such that in particular its module category has a natural vertex tensor category structure, and consequently, a natural braided… Expand

LAURENT EXPANSIONS IN CLUSTER ALGEBRAS VIA QUIVER REPRESENTATIONS

- A. Kirillov
- Mathematics
- 2006

We study Laurent expansions of cluster variables in a cluster algebra of rank 2 associated to a generalized Kronecker quiver. In the case of the ordinary Kronecker quiver, we obtain explicit… Expand

The universal rotation curve of spiral galaxies

- A. Kirillov, D. Turaev
- Physics
- 24 April 2006

The observed strong dark-to-luminous matter coupling is described by a bias relation between visible and dark matter sources. We discuss the bias which emerges in the case where the topological… Expand

On $G$--equivariant modular categories

- A. Kirillov
- Mathematics
- 12 January 2004

In this paper, we study $G$-equivariant tensor categories for a finite group $G$. These categories were introduced by Turaev under the name of $G$-crossed categories; the motivating example of such a… Expand

On the polynomial invariants of the elasticity tensor

- J. Boehler, A. Kirillov, E. Onat
- Mathematics
- 1 February 1994

We consider the old problem of finding a basis of polynomial invariants of the fourth rank tensorC of elastic moduli of an anisotropic material. DecomposingC into its irreducible components we reduce… Expand

Infinite dimensional lie groups; their orbits, invariants and representations. The geometry of moments

- A. Kirillov
- Mathematics
- 1982

Lectures on Representation Theory and Knizhnik-Zamolodchikov Equations

- P. Etingof, I. Frenkel, A. Kirillov
- Mathematics
- 16 June 1998

Introduction Representations of finite-dimensional and affine Lie algebras Knizhnik-Zamolodchikov equations Solutions of the Knizhnik-Zamolodchikov equations Free field realization Quantum groups… Expand

Spherical functions on affine Lie groups

- P. Etingof, I. Frenkel, A. Kirillov
- Mathematics
- 9 July 1994

We describe vector valued conjugacy equivariant functions on a group K in two cases -- K is a compact simple Lie group, and K is an affine Lie group.
We construct such functions as weighted traces… Expand

String-net model of Turaev-Viro invariants

- A. Kirillov
- Computer Science
- 29 June 2011

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