Invariants of the vacuum module associated with the Lie superalgebra gl(1|1)
| Autor: | Molev, A. I., Mukhin, E. E. |
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| Rok vydání: | 2015 |
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| Zdroj: | J. Phys. A: Math. Theor. 48 (2015) 314001 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1088/1751-8113/48/31/314001 |
| Popis: | We describe the algebra of invariants of the vacuum module associated with the affinization of the Lie superalgebra $\mathfrak{gl}(1|1)$. We give a formula for its Hilbert--Poincar\'{e} series in a fermionic (cancellation-free) form which turns out to coincide with the generating function of the plane partitions over the $(1,1)$-hook. Our arguments are based on a super version of the Beilinson--Drinfeld--Ra\"{i}s--Tauvel theorem which we prove by producing an explicit basis of invariants of the symmetric algebra of polynomial currents associated with $\mathfrak{gl}(1|1)$. We identify the invariants with affine supersymmetric polynomials via a version of the Chevalley theorem. Comment: 24 pages, final version; contribution to Rodney Baxter volume, J.Phys. A |
| Databáze: | arXiv |
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