Abstract
Making use of a Howe duality involving the infinite-dimensional Lie super-algebra gl∞|∞ and finite-dimensional group GLl of [CW3] we derive a character formula for a certain class of irreducible quasi-finite representations of gl∞|∞ in terms of hook Schur functions. We use the reduction procedure of gl∞|∞ to gln|n to derive a character formula for a certain class of level 1 highest weight irreducible representations of gln|n, the affine Lie superalgebra associated to the finite-dimensional Lie superalgebra gln|n. These modules turn out to form the complete set of integrable gln|n-modules of level 1. We also show that the characters of all integrable level 1 highest weight irreducible glm|n-modules may be written as a sum of products of hook Schur functions.
| Original language | English |
|---|---|
| Pages (from-to) | 95-118 |
| Number of pages | 24 |
| Journal | Communications in Mathematical Physics |
| Volume | 238 |
| Issue number | 1-2 |
| DOIs | |
| Publication status | Published - 2003 Jan 1 |
Fingerprint
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics
Cite this
}
Infinite-dimensional Lie superalgebras and hook Schur functions. / Cheng, Shun Jen; Lam, Ngau.
In: Communications in Mathematical Physics, Vol. 238, No. 1-2, 01.01.2003, p. 95-118.Research output: Contribution to journal › Article
TY - JOUR
T1 - Infinite-dimensional Lie superalgebras and hook Schur functions
AU - Cheng, Shun Jen
AU - Lam, Ngau
PY - 2003/1/1
Y1 - 2003/1/1
N2 - Making use of a Howe duality involving the infinite-dimensional Lie super-algebra gl∞|∞ and finite-dimensional group GLl of [CW3] we derive a character formula for a certain class of irreducible quasi-finite representations of gl∞|∞ in terms of hook Schur functions. We use the reduction procedure of gl∞|∞ to gln|n to derive a character formula for a certain class of level 1 highest weight irreducible representations of gln|n, the affine Lie superalgebra associated to the finite-dimensional Lie superalgebra gln|n. These modules turn out to form the complete set of integrable gln|n-modules of level 1. We also show that the characters of all integrable level 1 highest weight irreducible glm|n-modules may be written as a sum of products of hook Schur functions.
AB - Making use of a Howe duality involving the infinite-dimensional Lie super-algebra gl∞|∞ and finite-dimensional group GLl of [CW3] we derive a character formula for a certain class of irreducible quasi-finite representations of gl∞|∞ in terms of hook Schur functions. We use the reduction procedure of gl∞|∞ to gln|n to derive a character formula for a certain class of level 1 highest weight irreducible representations of gln|n, the affine Lie superalgebra associated to the finite-dimensional Lie superalgebra gln|n. These modules turn out to form the complete set of integrable gln|n-modules of level 1. We also show that the characters of all integrable level 1 highest weight irreducible glm|n-modules may be written as a sum of products of hook Schur functions.
UR - http://www.scopus.com/inward/record.url?scp=0038675125&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0038675125&partnerID=8YFLogxK
U2 - 10.1007/s00220-003-0819-3
DO - 10.1007/s00220-003-0819-3
M3 - Article
VL - 238
SP - 95
EP - 118
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
SN - 0010-3616
IS - 1-2
ER -