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 GLn, the two-parameter polynomial functors give a new interpretation of (polynomial) representations of the quantum symmetric pair (\( {U}_{Q,q}^B \)(\( \mathfrak{gl} \)n), Uq(\( \mathfrak{gl} \)n)) which specializes to type AIII/AIV quantum symmetric pairs. The coideal subalgebra \( {U}_{Q,q}^B \)(\( \mathfrak{gl} \)n) appears in a Schur–Weyl duality with the type B Hecke algebra \( {\mathcal{H}}_{Q,q}^B \)(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.
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Valentin Buciumas is supported by ARC grant DP180103150.
Hankyung Ko is supported by the Max Planck Institute for Mathematics in Bonn.
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BUCIUMAS, V., KO, H. POLYNOMIAL FUNCTORS AND TWO-PARAMETER QUANTUM SYMMETRIC PAIRS. Transformation Groups 28, 107–149 (2023). https://doi.org/10.1007/s00031-022-09716-w
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DOI: https://doi.org/10.1007/s00031-022-09716-w