Using the bases of principal subspaces for twisted affine Lie algebras except $A_{2l}^{(2)}$ by Butorac and Sadowski, we construct highest weight modules kΛ0 parafermionic spases same algebras. As a result, obtain their character formulas conjectured in Hatayama et al. (2001).

Let g be a finite-dimensional semisimple Lie algebra and (· , ·) its Killing form, σ an elliptic automorphism of g, and a a σ-invariant reductive subalgebra of g, such that the restriction of the form (· , ·) to a is non-degenerate. Let L̂(g, σ) and L̂(a, σ) be the associated twisted affine Lie algebras and F σ(p) the σ-twisted Clifford module over L̂(a, σ), associated to the orthocomplement p of ...

We generalize Feigin and Miwa’s construction of extended vertex operator (super)algebras Ak(sl(2)) for other types of simple Lie algebras. For all the constructed extended vertex operator (super)algebras, irreducible modules are classified, complete reducibility of every module is proved and fusion rules are determined modulo the fusion rules for vertex operator algebras of affine type.

We apply the construction of universal lower-bounded generalized twisted modules by author to construct and grading-restricted for affine vertex (operator) algebras. prove that these algebras are equivalent suitable induced corresponding Lie algebra or quotients such explicitly given submodules .

We study the classification problem for left-symmetric algebras with commutation Lie algebra gl(n) in characteristic 0. The problem is equivalent to the classification of étale affine representations of gl(n). Algebraic invariant theory is used to characterize those modules for the algebraic group SL(n) which belong to affine étale representations of gl(n). From the classification of these modu...

In this paper we present Affine.m — a program for computations in representation theory of finite-dimensional and affine Lie algebras and describe implemented algorithms. The algorithms are based on the properties of weights and Weyl symmetry. Computation of weight multiplicities in irreducible and Verma modules, branching of representations and tensor product decomposition are the most importa...

This paper provides a unified approach to results on representations of affine Hecke algebras, cyclotomic Hecke algebras, affine BMW algebras, cyclotomic BMW algebras, Markov traces, Jacobi-Trudi type identities, dual pairs [Ze], and link invariants [Tu2]. The key observation in the genesis of this paper was that the technical tools used to obtain the results in Orellana [Or] and Suzuki [Su], t...