Symmetric polynomials and

Author:
Naihuan Jing

Journal:
Represent. Theory **4** (2000), 46-63

MSC (2000):
Primary 17B; Secondary 5E

DOI:
https://doi.org/10.1090/S1088-4165-00-00065-0

Published electronically:
February 7, 2000

MathSciNet review:
1740180

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Abstract | References | Similar Articles | Additional Information

We study the explicit formula of Lusztig's integral forms of the level one quantum affine algebra in the endomorphism ring of symmetric functions in infinitely many variables tensored with the group algebra of . Schur functions are realized as certain orthonormal basis vectors in the vertex representation associated to the standard Heisenberg algebra. In this picture the Littlewood-Richardson rule is expressed by integral formulas, and is used to define the action of Lusztig's -form of on Schur polynomials. As a result the -lattice of Schur functions tensored with the group algebra contains Lusztig's integral lattice.

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Additional Information

**Naihuan Jing**

Affiliation:
Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695-8205

Email:
jing@math.ncsu.edu

DOI:
https://doi.org/10.1090/S1088-4165-00-00065-0

Keywords:
Symmetric functions,
vertex operators,
quantum affine algebras,
Littlewood-Richardson rule

Received by editor(s):
February 17, 1999

Received by editor(s) in revised form:
December 10, 1999

Published electronically:
February 7, 2000

Additional Notes:
Research supported in part by NSA grant MDA904-97-1-0062 and Mathematical Sciences Research Institute.

Article copyright:
© Copyright 2000
American Mathematical Society