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2. Classification of the reducible Verma modules over the Jacobi algebra G2.

Author

Aizawa, N, Dobrev, V K, and Doi, S

Subjects
*ALGEBRA, *REPRESENTATIONS of algebras, *LIE algebras, *CLASSIFICATION, *INDECOMPOSABLE modules, *JACOBI polynomials
Abstract

In the present paper we study the representations of the Jacobi algebra. More concretely, we define, analogously to the case of semi-simple Lie algebras, the Verma modules over the Jacobi algebra G 2 . We study their reducibility and give explicit construction of the reducible Verma modules exhibiting the corresponding singular vectors. Using this information we give a complete classification of the reducible Verma modules. More than this we exhibit their interrelation of embeddings between these modules. These embeddings are illustrated by diagrams of the embedding patterns so that each reducible Verma module appears in one such diagram. [ABSTRACT FROM AUTHOR]

Published
2021
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26. Explicit character formulae for positive energy unitary irreducible representations of D = 4 conformal supersymmetry.

Author

Dobrev, V. K.

Subjects
*UNITARY dynamics, *SUPERSYMMETRY, *SUPERALGEBRAS, *FIELD theory (Physics), *CONFORMAL geometry
Abstract

This paper continues the project of constructing the character formulae for the positive energy unitary irreducible representations of the N-extended D = 4 conformal superalgebras su(2, 2/N). In the first paper we gave the bare characters which represent the defining odd entries of the characters. Now we give the full explicit character formulae for N = 1 and for several important examples for N = 2 and N = 4. [ABSTRACT FROM AUTHOR]

Published
2013
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