A new realisation of the i-quantum group U(n)

Abstract

We follow the approach developed in [3] and modified in [7] to investigate a new realisation for the i -quantum groups U ȷ ( n ) , building on the multiplication formulas discovered in [2, Lem. 3.2] . This allows us to present U ȷ ( n ) via a basis and multiplication formulas by generators. We also establish a surjective algebra homomorphism from a Lusztig type form U Z ȷ ( n ) of U ȷ ( n ) to the integral q -Schur algebras S Z ȷ ( n , r ) of type B . Thus, base change to a field k allows us to relate representations of the i -quantum hyperalgebras U k ȷ ( n ) to representations of finite orthogonal groups of odd degree in non-defining characteristics. This generalises part of Dipper–James' type A theory to the type B case.