SYMMETRIC POLYNOMIALS AND Uq ( ̂ sl2)
نویسنده
چکیده
We study the explicit formula of Lusztig’s integral forms of the level one quantum affine algebra Uq(ŝl2) in the endomorphism ring of symmetric functions in infinitely many variables tensored with the group algebra of Z. 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 Z[q, q]-form of Uq(ŝl2) on Schur polynomials.
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