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 [email protected]
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