Gelfand-Zetlin basis, whittaker vectors and a bosonic formula for the sln+1 principal subspace

B. Feigin; M. Jimbo; T. Miwa

doi:10.2977/PRIMS/42

Gelfand-Zetlin basis, whittaker vectors and a bosonic formula for the sl_n+1 principal subspace

B. Feigin^*
, M. Jimbo
, T. Miwa

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We derive a bosonic formula for the character of the principal space in the level k vacuum module for sl_n+1, starting from a known fermionic formula for it. In our previous work, the latter was written as a sum consisting of Shapovalov scalar products of Whittaker vectors for Uv ±1 (gl_n+1). In this paper we compute these scalar products in bosonic form, using the decomposition of Whittaker vectors in the Gelfand-Zetlin basis. We show further that the bosonic formula obtained in this way is the quasi-classical decomposition of the fermionic formula.

Original language	English
Pages (from-to)	535-551
Number of pages	17
Journal	Publications of the Research Institute for Mathematical Sciences
Volume	47
Issue number	2
DOIs	https://doi.org/10.2977/PRIMS/42
State	Published - 2011
Externally published	Yes

Keywords

Bosonic formulas
Diference toda hamiltonian
Fermionic formulas
Quantum groups

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abstract = "We derive a bosonic formula for the character of the principal space in the level k vacuum module for sln+1, starting from a known fermionic formula for it. In our previous work, the latter was written as a sum consisting of Shapovalov scalar products of Whittaker vectors for Uv ±1 (gln+1). In this paper we compute these scalar products in bosonic form, using the decomposition of Whittaker vectors in the Gelfand-Zetlin basis. We show further that the bosonic formula obtained in this way is the quasi-classical decomposition of the fermionic formula.",

keywords = "Bosonic formulas, Diference toda hamiltonian, Fermionic formulas, Quantum groups",

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AU - Feigin, B.

AU - Jimbo, M.

AU - Miwa, T.

PY - 2011

Y1 - 2011

N2 - We derive a bosonic formula for the character of the principal space in the level k vacuum module for sln+1, starting from a known fermionic formula for it. In our previous work, the latter was written as a sum consisting of Shapovalov scalar products of Whittaker vectors for Uv ±1 (gln+1). In this paper we compute these scalar products in bosonic form, using the decomposition of Whittaker vectors in the Gelfand-Zetlin basis. We show further that the bosonic formula obtained in this way is the quasi-classical decomposition of the fermionic formula.

AB - We derive a bosonic formula for the character of the principal space in the level k vacuum module for sln+1, starting from a known fermionic formula for it. In our previous work, the latter was written as a sum consisting of Shapovalov scalar products of Whittaker vectors for Uv ±1 (gln+1). In this paper we compute these scalar products in bosonic form, using the decomposition of Whittaker vectors in the Gelfand-Zetlin basis. We show further that the bosonic formula obtained in this way is the quasi-classical decomposition of the fermionic formula.

KW - Bosonic formulas

KW - Diference toda hamiltonian

KW - Fermionic formulas

KW - Quantum groups

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JO - Publications of the Research Institute for Mathematical Sciences

JF - Publications of the Research Institute for Mathematical Sciences

IS - 2

ER -

Gelfand-Zetlin basis, whittaker vectors and a bosonic formula for the sl_n+1 principal subspace

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Keywords

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