## University of Sydney Algebra Seminar

# Pavel Pyatov (SU-HSE, Moscow)

## Friday 30th July, 12.05-12.55pm, Carslaw 175

### Quasi-oscillator presentation for the quantum group Uq(gl(N))

Introducing spectral values for the L-matrices (where L is a matrix of generators for the reflection equation algebra) we define the spectral extension of the QUE algebra U_q(gl(N)). The set of spectral values generates a maximal commutative subalgebra of the extended U_q(gl(N)). Supplementing each spectral value with a pair of "raising" and "lowering" operators we obtain a quasi-oscillator presentation for the extended QUE algebra. Finally, expressing the L-matrix in terms of the quasi-oscillators we open a possibility for applications of the quasi-oscillator set to investigations of quantum integrable chains.

This is joint work with Igor Kozhanov.