Character formula for infinite-dimensional unitarizable modules of the general linear superalgebra

Shun Jen Cheng; Ngau Lam; R. B. Zhang

doi:10.1016/S0021-8693(03)00538-6

Character formula for infinite-dimensional unitarizable modules of the general linear superalgebra

Shun Jen Cheng, Ngau Lam, R. B. Zhang

Department of Mathematics

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

23 Citations (Scopus)

Abstract

The Fock space of m + p bosonic and n + q fermionic quantum oscillators forms a unitarizable module of the general linear superalgebra gl_{m+p n+q}. Its tensor powers decompose into direct sums of infinite-dimensional irreducible highest-weight gl_{m+p n+q}-modules. We obtain an explicit decomposition of any tensor power of this Fock space into irreducibles, and develop a character formula for the irreducible gl_{m+p n+q}-modules arising in this way.

Original language	English
Pages (from-to)	780-805
Number of pages	26
Journal	Journal of Algebra
Volume	273
Issue number	2
DOIs	https://doi.org/10.1016/S0021-8693(03)00538-6
Publication status	Published - 2004 Mar 15

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1016/S0021-8693(03)00538-6

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title = "Character formula for infinite-dimensional unitarizable modules of the general linear superalgebra",

abstract = "The Fock space of m + p bosonic and n + q fermionic quantum oscillators forms a unitarizable module of the general linear superalgebra glm+p n+q. Its tensor powers decompose into direct sums of infinite-dimensional irreducible highest-weight glm+p n+q-modules. We obtain an explicit decomposition of any tensor power of this Fock space into irreducibles, and develop a character formula for the irreducible glm+p n+q-modules arising in this way.",

author = "Cheng, {Shun Jen} and Ngau Lam and Zhang, {R. B.}",

note = "Funding Information: * Corresponding author. E-mail addresses: [email protected] (S.-J. Cheng), [email protected] (N. Lam), [email protected] (R.B. Zhang). 1 Partially supported by NSC-grant 91-2115-M-002-007 of the ROC. 2 Partially supported by NSC-grant 91-2115-M-006-013 of the ROC. 3 Supported by the Australian Research Council.",

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doi = "10.1016/S0021-8693(03)00538-6",

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AU - Cheng, Shun Jen

AU - Lam, Ngau

AU - Zhang, R. B.

N1 - Funding Information: * Corresponding author. E-mail addresses: [email protected] (S.-J. Cheng), [email protected] (N. Lam), [email protected] (R.B. Zhang). 1 Partially supported by NSC-grant 91-2115-M-002-007 of the ROC. 2 Partially supported by NSC-grant 91-2115-M-006-013 of the ROC. 3 Supported by the Australian Research Council.

PY - 2004/3/15

Y1 - 2004/3/15

N2 - The Fock space of m + p bosonic and n + q fermionic quantum oscillators forms a unitarizable module of the general linear superalgebra glm+p n+q. Its tensor powers decompose into direct sums of infinite-dimensional irreducible highest-weight glm+p n+q-modules. We obtain an explicit decomposition of any tensor power of this Fock space into irreducibles, and develop a character formula for the irreducible glm+p n+q-modules arising in this way.

AB - The Fock space of m + p bosonic and n + q fermionic quantum oscillators forms a unitarizable module of the general linear superalgebra glm+p n+q. Its tensor powers decompose into direct sums of infinite-dimensional irreducible highest-weight glm+p n+q-modules. We obtain an explicit decomposition of any tensor power of this Fock space into irreducibles, and develop a character formula for the irreducible glm+p n+q-modules arising in this way.

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Character formula for infinite-dimensional unitarizable modules of the general linear superalgebra

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