Type: Seminar

Distribution: World

Expiry: 19 Jul 2017

CalTitle1: Algebra Seminar: Noncommutative classical invariant theory for the quantum general linear supergroup

Auth: kevinc@120.88.165.116 (kcou7211) in SMS-WASM

Yang Zhang (University of Sydney) Friday 9 June, 12-1pm, Place: Carslaw 375 Title: Noncommutative classical invariant theory for the quantum general linear supergroup Abstract: We will give the noncommutative polynomial version of the invariant theory for the quantum general linear supergroup U_q(gl_{m|n}). A noncommutative U_q(gl_{m|n})-module superalgebra P^{k|l}_{r|s} is constructed, which is the quantum analogue of the supersymmetric algebra over C^{k|l}\otimes C^{m|n}\oplus C^{r|s}\otimes (C^{m|n})*. The subalgebra of U_q(gl_{m|n})-invariants in P^{k|l}_{r|s} is shown to be finitely generated. We determine its generators and establish a surjective superalgebra homomorphism from a braided supersymmetric algebra onto it. This establishes the first fundamental theorem (FFT) of invariant theory for U_q(gl_{m|n}). When the above homomorphism is not injective, we give a representation theoretical description of the generating elements of the kernel associated to the partition ((m+1)^{n+1}), which amounts to the second fundamental theorem (SFT) of invariant theory for U_q(gl_{m|n}). Applications to the quantum general linear group U_q(gl_m) and the general linear superalgebra gl_{m|n} will also be discussed.