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• W2941640203 abstract "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 ( $$ {U}_{Q,q}^B $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msubsup> <mml:mi>U</mml:mi> <mml:mrow> <mml:mi>Q</mml:mi> <mml:mo>,</mml:mo> <mml:mi>q</mml:mi> </mml:mrow> <mml:mi>B</mml:mi> </mml:msubsup> </mml:math> ( $$ mathfrak{gl} $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>gl</mml:mi> </mml:math> n ), U q ( $$ mathfrak{gl} $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>gl</mml:mi> </mml:math> n )) which specializes to type AIII/AIV quantum symmetric pairs. The coideal subalgebra $$ {U}_{Q,q}^B $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msubsup> <mml:mi>U</mml:mi> <mml:mrow> <mml:mi>Q</mml:mi> <mml:mo>,</mml:mo> <mml:mi>q</mml:mi> </mml:mrow> <mml:mi>B</mml:mi> </mml:msubsup> </mml:math> ( $$ mathfrak{gl} $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>gl</mml:mi> </mml:math> n ) appears in a Schur–Weyl duality with the type B Hecke algebra $$ {mathcal{H}}_{Q,q}^B $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msubsup> <mml:mi>H</mml:mi> <mml:mrow> <mml:mi>Q</mml:mi> <mml:mo>,</mml:mo> <mml:mi>q</mml:mi> </mml:mrow> <mml:mi>B</mml:mi> </mml:msubsup> </mml:math> ( 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." @default.
• W2941640203 created "2019-05-03" @default.
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• W2941640203 date "2022-03-31" @default.
• W2941640203 modified "2023-09-26" @default.
• W2941640203 title "POLYNOMIAL FUNCTORS AND TWO-PARAMETER QUANTUM SYMMETRIC PAIRS" @default.
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