The i-Quantum Group $$\textbf{U}^\imath (n)$$, II: Presenting their $$\varvec{q}$$-Schur Algebras
Year: 2026
Type: article
Abstract: Since the establishment of the quantum Schur–Weyl duality in Jimbo (Lett. Math. Phys. 11 , 247–252, 1986), the duality pair $$(\textbf{U}(\mathfrak {gl}_n),\varvec{\mathcal {H}}(\mathfrak S_r))$$ ( U ( gl n ) , H ( S r ) ) of type A has been extended to the duality pairs $$(\textbf{U}^\jmath (n),\varvec{\mathcal {H}}(B_r))$$ ( U ȷ ( n ) , H ( B r ) ) and $$(\textbf{U}^\imath (n),\varvec{\mathcal {H}}(C_r))$$ ( U ı ( n ) , H ( C r ) ) in the Hecke algebra series in Bao and Wang (Astérisque 402 , vii+134, 2018), where $$\textbf{U}^\jmath (n),\textbf{U}^\imath (n)$$ U ȷ ( n ) , U ı ( n ) are i -quantum groups arising from certain quantum symmetric pairs. The quantum Schur algebra associated with the pair $$(\textbf{U}(\mathfrak {gl}_n),\varvec{\mathcal {H}}(\mathfrak S_r))$$ ( U ( gl n ) , H ( S r ) ) has a nice and simple presentation; see Doty and Giaquinto (2002). In this paper, we tackle the presentation problem for the i -quantum Schur algebras associated with the duality pair $$(\textbf{U}^\imath (n),\varvec{\mathcal {H}}(C_r))$$ ( U ı ( n ) , H ( C r ) ) . Suc
Authors: Jian Chen, Jie Du
Institutions: East China Normal University, UNSW Sydney
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,490
Funder: University of New South Wales
OpenAlex ID: W7154305230