Twisted Yangians and Mickelsson Algebras II
Sergey Khoroshkin, Maxim Nazarov
TL;DR
This paper develops a new skew analogue of functors for twisted Yangians based on skew Howe duality, establishing a correspondence between intertwining operators and extremal cocycles, advancing the algebraic understanding of twisted Yangians.
Contribution
It introduces a novel skew analogue of the Cherednik and Drinfeld functors for twisted Yangians, rooted in skew Howe duality and the centralizer construction.
Findings
Established a correspondence between intertwining operators and extremal cocycles.
Connected the skew analogue functor to the centralizer construction of twisted Yangians.
Extended the algebraic framework for twisted Yangians using skew Howe duality.
Abstract
We introduce a skew analogue of the composition of the Cherednik and Drinfeld functors for twisted Yangians. Our definition is based on the skew Howe duality, and originates from the centralizer construction of twisted Yangians due to Olshanski. Using our functor, we establish a correspondence between intertwining operators on the tensor products of certain modules over twisted Yangians, and the extremal cocycle on the hyperoctahedral group.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Algebra and Logic · Advanced Operator Algebra Research