POLYNOMIAL FUNCTORS AND TWO-PARAMETER QUANTUM SYMMETRIC PAIRS
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- Title
- POLYNOMIAL FUNCTORS AND TWO-PARAMETER QUANTUM SYMMETRIC PAIRS
- Authors
- BUCIUMAS, VALENTIN; KO, HANKYUNG
- Date Issued
- 2023-03
- Publisher
- Birkhaeuser
- Abstract
- We develop a theory of two-parameter quantum polynomial functors. Similar to how (strict) polynomial functors give a new interpretation of polynomial representations of the general linear groups GL(n), the two-parameter polynomial functors give a new interpretation of (polynomial) representations of the quantum symmetric pair (U-Q,q(B)(gl(n)), U-q(gl(n))) which specializes to type AIII/AIV quantum symmetric pairs. The coideal subalgebra U-Q,q(B) (gl(n)) appears in a Schur-Weyl duality with the type B Hecke algebra H-Q,q(B) (d). We endow two-parameter polynomial functors with a cylinder braided structure which we use to construct the two-parameter Schur functors. Our polynomial functors can be precomposed with the quantum polynomial functors of type A producing new examples of action pairs.
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/120747
- DOI
- 10.1007/s00031-022-09716-w
- ISSN
- 1083-4362
- Article Type
- Article
- Citation
- Transformation Groups, vol. 28, no. 1, page. 107 - 149, 2023-03
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