Finite-dimensional irreducible representations of twisted loop algebras of the second kind are classified by explicit highest-weight power-sum formulas, proved elementarily for four minimal algebras and assembled in a general theorem.
Affine $\imath$quantum groups and twisted Yangians in Drinfeld presentations
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We formulate a family of algebras, twisted Yangians (of split type) in current generators and relations, via a degeneration of the Drinfeld presentation of affine $\imath$quantum groups (associated with split Satake diagrams). These new algebras admit PBW type bases and are shown to be a deformation of twisted current algebras; presentations for twisted current algebras are also provided. For type AI, it matches with the Drinfeld presentation of twisted Yangian obtained via Gauss decomposition. We conjecture that our split twisted Yangians are isomorphic to the corresponding ones in RTT presentation.
fields
math.RT 1years
2025 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
Finite-dimensional irreducible representations of twisted loop algebras of the second kind
Finite-dimensional irreducible representations of twisted loop algebras of the second kind are classified by explicit highest-weight power-sum formulas, proved elementarily for four minimal algebras and assembled in a general theorem.