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Combinatorial bases for covariant representations of the Lie superalgebra gl(m|n)
| Content Provider | Semantic Scholar |
|---|---|
| Author | Molev, A. I. |
| Copyright Year | 2010 |
| 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 and give explicit formulas for the action of the generators of gl(m|n) in this basis. The basis has the property that the natural Lie subalgebras gl(m) and gl(n) act 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. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://w3.math.sinica.edu.tw/bulletin_ns/20114/2011402.pdf |
| Alternate Webpage(s) | http://www.maths.usyd.edu.au/u/pubs/publist/preprints/2010/molev-27.pdf |
| Alternate Webpage(s) | https://arxiv.org/pdf/1010.0463v2.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
