Abstract
We study the explicit formula of Lusztig’s integral forms of the level one quantum affine algebraUq(sl^2)U_q(\widehat {sl}_2)in the endomorphism ring of symmetric functions in infinitely many variables tensored with the group algebra ofZ\mathbb 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’sZ[q,q−1]\mathbb Z[q, q^{-1}]-form ofUq(sl^2)U_q(\widehat {sl}_2)on Schur polynomials. As a result theZ[q,q−1]\mathbb Z[q, q^{-1}]-lattice of Schur functions tensored with the group algebra contains Lusztig’s integral lattice.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Representation Theory of the American Mathematical Society
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
