相关论文: A representation theoretic approach to the WZW Ver…
On the bundles of WZW chiral blocks over the moduli space of a punctured rational curve we construct isomorphisms that implement the action of outer automorphisms of the underlying affine Lie algebra. These bundle-isomorphisms respect the…
We survey some important results concerning the finite--dimensional representations of the loop algebra of a simple complex Lie algebra, and their twisted loop subalgebras. In particular, we review the parametrization and description of the…
This is an expository article on representation theory of toroidal Lie algebras. We summerize all the results on representation theory of toroidal Lie algebras obtained in the last fifteen years. Apart from that a natural genaralization of…
We construct irreducible modules of centrally-extended classical Lie algebras over left ideals of the algebra of differential operators on the circle, through certain irreducible modules of centrally-extended classical Lie algebras of…
In this paper, we construct various simple vertex superalgebras which are extensions of affine vertex algebras, by using abelian cocycle twists of representation categories of quantum groups. This solves the Creutzig and Gaiotto conjectures…
The Verlinde formula computes the dimension of certain vector spaces ("conformal blocks") associated to a Rational Conformal Field Theory. In this paper we show how this can be made rigorous for one particular such theory, the WZW model.…
The Toroidal Lie algebras are n variable genaralizations of Affine Kac-Moody Lie algebras. As in the affine Lie algebras there exists finite order auto= morphisms corresponding to Dynkin diagram automorphisms. The fixed point sub= algebras…
In this note we illustrate by a few examples the general principle: interesting algebras and representations defined over Z_+ come from category theory, and are best understood when their categorical origination has been discovered. We show…
The Brylinski-Kostant filtration on a representation of a finite-dimensional semisimple Lie algebra has interpretations in terms of the algebra, geometry and combinatorics of the representation. Its extension to affine Lie algebras was…
In this paper we construct a geometric analogue of the Weil representation over a finite field. Our construction is principally invariant, not choosing any specific realization. This eliminates most of the unpleasant formulas that appear in…
Affine W-algebras are a somewhat complicated family of (topological) associative algebras associated with a semisimple Lie algebra, quantizing functions on the algebraic loop space of Kostant's slice. They have attracted a great deal of…
The Weil representation of the symplectic group associated to a finite abelian group of odd order is shown to have a multiplicity-free decomposition. When the abelian group is p-primary, the irreducible representations occurring in the Weil…
The coefficient algebra of a finite-dimensional Lie algebra on a finite-dimensional representation is defined as the subalgebra generated by all coefficients of the corresponding characteristic polynomial. We explore connections between…
Much of the work in loop quantum gravity and quantum geometry rests on a mathematically rigorous integration theory on spaces of distributional connections. Most notably, a diffeomorphism invariant representation of the algebra of basic…
Let ${\mathcal O}$ be an involutive discrete valuation ring with residue field of characteristic not 2. Let $A$ be a quotient of ${\mathcal O}$ by a nonzero power of its maximal ideal and let $*$ be the involution that $A$ inherits from…
Much of the work in loop quantum gravity and quantum geometry rests on a mathematically rigorous integration theory on spaces of distributional connections. Most notably, a diffeomorphism invariant representation of the algebra of basic…
We study representations of the double affine Lie algebra associated to a simple Lie algebra. We construct a family of indecomposable integrable representations and identify their irreducible quotients. We also give a condition for the…
We construct irreducible modules for twisted toroidal Lie algebras and extended affine Lie algebras. This is done by combining the representation theory of untwisted toroidal algebras with the technique of thin coverings of modules. We…
Suppose a finite group acts on a scheme $X$ and a finite-dimensional Lie algebra $\mathfrak{g}$. The associated equivariant map algebra is the Lie algebra of equivariant regular maps from $X$ to $\mathfrak{g}$. The irreducible…
Toroidal Lie algebras are $n$ variable generalizations of affine Kac-Moody Lie algebras. Full toroidal Lie algebra is the semidirect product of derived Lie algebra of toroidal Lie algebra and Witt algebra, also it can be thought of…