**SMS scnews item created by James East at Wed 28 Jul 2010 1222**

Type: Seminar

Distribution: World

Expiry: 30 Jul 2010

**Calendar1: 30 Jul 2010 1205-1255**

**CalLoc1: Carslaw 175**

Auth: jamese@bari.maths.usyd.edu.au

### Algebra Seminar

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

### Pavel Pyatov

#### Friday July 30, 12:05--12:55pm, Carslaw 175

###### Abstract

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.

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After the seminar we will take the speaker to lunch.

See the Algebra Seminar web page for information about other seminars in the series.

James East james.east@sydney.edu.au