**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**

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

### Algebra Seminar

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

### Alex Molev

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

###### Abstract

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.

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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

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