SMS scnews item created by James East at Mon 22 Nov 2010 1006
Type: Seminar
Modified: Mon 22 Nov 2010 1007
Distribution: World
Expiry: 26 Nov 2010
Calendar1: 26 Nov 2010 1205-1255
CalLoc1: Carslaw 175

Algebra Seminar

Combinatorial bases for representations of the Lie superalgebra gl(m|n)

Alex Molev

Friday Movember 26, 12:05--12:55pm, Carslaw 175


Covariant tensor representations of gl(m|n) occur as irreducible components of tensor powers of the natural (m+n)-dimensional representation. We construct a basis of each covariant representation which has the property that the natural Lie subalgebras gl(m) and gl(n) act in this basis by the classical Gelfand-Tsetlin formulas. The main role in the construction is played by the fact that the subspace of gl(m)-highest vectors in any finite-dimensional irreducible representation of gl(m|n) carries a structure of an irreducible module over the Yangian Y(gl(n)). One consequence is a new proof of the character formula for the covariant representations first found by Berele and Regev and by Sergeev.


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

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