Symmetric Polynomials and $U_q(\hat{sl}_2)$

We study the explicit formula of Lusztig’s integral forms of the level one quantum affine algebra $U_{q} ({\hat{s l}}_{2})$ 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 $U_{q} ({\hat{s l}}_{2})$ on Schur polynomials.

Symmetric Polynomials and $U_{q} ({\hat{s l}}_{2})$

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Symmetric Polynomials and $U_{q} ({\hat{s l}}_{2})$

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Symmetric Polynomials and Uq(sl^2)Uq​(sl^2​)

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Symmetric Polynomials and Uq(sl^2)Uq​(sl^2​)

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Symmetric Polynomials and $U_{q} ({\hat{s l}}_{2})$

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Symmetric Polynomials and $U_{q} ({\hat{s l}}_{2})$

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