Finite-dimensional irreducible representations of twisted loop algebras of the second kind

2025/06/03 by Hideya Watanabe, Watanabe, Hideya
Mathematics · Computer Science · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.2506.02379

Abstract

Twisted loop algebras of the second kind are infinite-dimensional Lie algebras that are constructed from a semisimple Lie algebra and an automorphism on it of order at most 2. They are examples of equivariant map algebras. The finite-dimensional irreducible representations of an arbitrary equivariant map algebra have been classified by Neher--Savage--Senesi. In this paper, we classify the finite-dimensional irreducible representations of twisted loop algebras of the second kind in a more elementary way.

Citations

• Boundary q-characters of evaluation modules for split quantum affine symmetric pairs
• Kirillov-Reshetikhin modules and quantum K-matrices
• Trigonometric K-matrices for finite-dimensional representations of quantum affine algebras
• The augmented tridiagonal algebra
• Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition

Related

• Finite-dimensional representation theory of loop algebras: a survey
• A block decomposition of finite-dimensional representations of twisted loop algebras
• Classification of irreducible integrable representations of loop\n toroidal Lie algebras
• Extensions des modules de dimension finie pour les algèbres de courants tordues
• Representations of twisted current algebras