scholarly journals Branching Functions for Admissible Representations of Affine Lie Algebras and Super-Virasoro Algebras

Axioms ◽  
2019 ◽  
Vol 8 (3) ◽  
pp. 82 ◽  
Author(s):  
Namhee Kwon
Keyword(s):  
Tensor Product ◽  
Lie Algebras ◽  
Affine Lie Algebras ◽  
Series Representations ◽  
Level 2

We explicitly calculate the branching functions arising from the tensor product decompositions between level 2 and principal admissible representations over sl ^ 2 . In addition, investigating the characters of the minimal series representations of super-Virasoro algebras, we present the tensor product decompositions in terms of the minimal series representations of super-Virasoro algebras for the case of principal admissible weights.

scholarly journals ON THE SPECTRA OF ${{\widehat{sl}\left( N \right)_k } \mathord{\left/ {\vphantom {{\widehat{sl}\left( N \right)_k } {\widehat{sl}\left( N \right)_k }}} \right. \kern-\nulldelimiterspace} {\widehat{sl}\left( N \right)_k }}$ AND WN GRAVITIES

1993 ◽  
Vol 08 (29) ◽  
pp. 5115-5128
Author(s):  
VLADIMIR SADOV
Keyword(s):  
Tensor Product ◽  
Lie Algebras ◽  
Hamiltonian Reduction ◽  
Affine Lie Algebras ◽  
Brst Cohomology ◽  
Boundary States ◽  
One To One ◽  
Coset Models

We study the spectra of G/G coset models by computing BRST cohomology of affine Lie algebras with coefficients in tensor product of two modules. One-to-one correspondence between the spectra of [Formula: see text] and that of the minimal matter coupled to gravity (including boundary states of the Kac table) is observed. This phenomenon is discussed from the point of Hamiltonian reduction of BRST complexes of [Formula: see text] Lie algebras.

The Cubic Dirac Operator for Infinite-Dimensonal Lie Algebras

2011 ◽  
Vol 63 (6) ◽  
pp. 1364-1387 ◽  
Author(s):  
Eckhard Meinrenken
Keyword(s):  
Dirac Operator ◽  
Tensor Product ◽  
Lie Algebras ◽  
Clifford Algebras ◽  
Symmetric Bilinear Form ◽  
Affine Lie Algebras ◽  
Weil Algebra ◽  
Casimir Element ◽  
Infinite Dimensional ◽  
Graded Lie Algebra

AbstractLet be an infinite-dimensional graded Lie algebra, with dim , equipped with a non-degenerate symmetric bilinear form B of degree 0. The quantum Weil algebra is a completion of the tensor product of the enveloping and Clifford algebras of g. Provided that the Kac–Peterson class of g vanishes, one can construct a cubic Dirac operator D 2 , whose square is a quadratic Casimir element. We show that this condition holds for symmetrizable Kac– Moody algebras. Extending Kostant's arguments, one obtains generalized Weyl–Kac character formulas for suitable “equal rank” Lie subalgebras of Kac–Moody algebras. These extend the formulas of G. Landweber for affine Lie algebras.

A class of non-standard modules for affine Lie algebras

1987 ◽  
Vol 196 (3) ◽  
pp. 303-313 ◽  
Author(s):  
Nolan R. Wallach
Keyword(s):  
Lie Algebras ◽  
Affine Lie Algebras

QUANTUM HAMILTONIAN REDUCTION AND WB ALGEBRA

1992 ◽  
Vol 07 (20) ◽  
pp. 4885-4898 ◽  
Author(s):  
KATSUSHI ITO
Keyword(s):  
Lie Algebras ◽  
Free Field ◽  
Lie Superalgebra ◽  
Lie Superalgebras ◽  
Hamiltonian Reduction ◽  
Affine Lie Algebras ◽  
Quantum Hamiltonian Reduction ◽  
Free Field Realization ◽  
Coset Construction ◽  
Quantum Hamiltonian

We study the quantum Hamiltonian reduction of affine Lie algebras and the free field realization of the associated W algebra. For the nonsimply laced case this reduction does not agree with the usual coset construction of the W minimal model. In particular, we find that the coset model [Formula: see text] can be obtained through the quantum Hamiltonian reduction of the affine Lie superalgebra B(0, n)(1). To show this we also construct the Feigin-Fuchs representation of affine Lie superalgebras.

scholarly journals Braided Tensor Categories of Admissible Modules for Affine Lie Algebras

2018 ◽  
Vol 362 (3) ◽  
pp. 827-854 ◽  
Author(s):  
Thomas Creutzig ◽  
Yi-Zhi Huang ◽  
Jinwei Yang
Keyword(s):  
Lie Algebras ◽  
Affine Lie Algebras ◽  
Tensor Categories
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