SMS scnews item created by Kevin Coulembier at Wed 24 May 2017 1506
Type: Seminar
Distribution: World
Expiry: 19 Jul 2017
Calendar1: 9 Jun 2017 1200-1300
CalLoc1: Carslaw 375
CalTitle1: Algebra Seminar: Noncommutative classical invariant theory for the quantum general linear supergroup
Auth: kevinc@120.88.165.116 (kcou7211) in SMS-WASM

# Algebra Seminar: Zhang -- Noncommutative classical invariant theory for the quantum general linear supergroup

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.


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