# Parafermionic bases of standard modules for twisted affine Lie algebras of type $A_{2l-1}^{(2)}$, $D_{l+1}^{(2)}$, $E_6^{(2)}$ and $D_4^{(3)}$

@inproceedings{Okado2021ParafermionicBO, title={Parafermionic bases of standard modules for twisted affine Lie algebras of type \$A\_\{2l-1\}^\{(2)\}\$, \$D\_\{l+1\}^\{(2)\}\$, \$E\_6^\{(2)\}\$ and \$D\_4^\{(3)\}\$}, author={Masato Okado and Ryo Takenaka}, year={2021} }

Using the bases of principal subspaces for twisted affine Lie algebras except A (2) 2l by Butorac and Sadowski, we construct bases of the highest weight modules of highest weight kΛ0 and parafermionic spases for the same affine Lie algebras. As a result, we obtain their character formulas conjectured in [14].

#### References

SHOWING 1-10 OF 26 REFERENCES

Combinatorial bases of principal subspaces of modules for twisted affine Lie algebras of type A ( 2 ) 2 l − 1 , D ( 2 ) l , E ( 2 ) 6 and D ( 3 ) 4

- 2019

We construct combinatorial bases of principal subspaces of standard modules of level k ≥ 1 with highest weight kΛ0 for the twisted affine Lie algebras of type A (2) 2l−1, D (2) l , E (2) 6 and D (3)… Expand

Vertex-algebraic structure of principal subspaces of standard A_2^{(2)}-modules, I

- Mathematics
- 2014

Extending earlier work of the authors, this is the first in a series of papers devoted to the vertex-algebraic structure of principal subspaces of standard modules for twisted affine Kac-Moody… Expand

Vertex algebraic structure of principal subspaces of basic A2n(2)-modules

- Mathematics
- 2016

Abstract We obtain a presentation of the principal subspace of the basic A 2 n ( 2 ) -module, n ≥ 1 . We show that its full character is given by the Nahm sum of the tadpole Dynkin diagram T n = A 2… Expand

Combinatorial constructions of modules for infinite-dimensional Lie algebras, I. Principal subspace

- Physics, Mathematics
- 1994

This is the first of a series of papers studying combinatorial (with no “subtractions”) bases and characters of standard modules for affine Lie algebras, as well as various subspaces and “coset… Expand

Structure of the standard modules for the affine Lie algebra A[(1)] [1]

- Mathematics
- 1985

The Lie algebra $A_1^(1)$ The category $\cal P_k$ The generalized commutation relations Relations for standard modules Basis of $\Omega_L$ for a standard module $L$ Schur functions Proof of linear… Expand

The algebraic structure of relative twisted vertex operators

- Mathematics, Physics
- 1996

Abstract Twisted vertex operators based on rational lattices have had many applications in vertex operator algebra theory and conformal field theory. In this paper, “relativized” twisted vertex… Expand

ON ABELIAN COSET GENERALIZED VERTEX ALGEBRAS

- Mathematics
- 2000

This paper studies the algebraic aspect of a general abelian coset theory with a work of Dong and Lepowsky as our main motivation. It is proved that the vacuum space ΩV (or the space of highest… Expand

A note on principal subspaces of the affine Lie algebras in types and

- Mathematics
- 2020

Abstract We construct quasi-particle bases of principal subspaces of standard modules where and Λj denotes the fundamental weight of affine Lie algebras of type or of level one. From the given bases… Expand

Calculus of twisted vertex operators.

- Mathematics, Medicine
- Proceedings of the National Academy of Sciences of the United States of America
- 1985

Starting from an arbitrary isometry of an arbitrary even lattice, twisted and shifted vertex operators are introduced. Under commutators, these operators provide realizations of twisted affine Lie… Expand

Characters in Conformal Field Theories from Thermodynamic Bethe Ansatz

- Physics
- 1993

We propose a new $q$-series formula for a character of parafermion conformal field theories associated to arbitrary non-twisted affine Lie algebra $\widehat{g}$. We show its natural origin from a… Expand