Ribbon Tableaux, HallLittlewood Functions, Quantum Affine Algebras and Unipotent Varieties
Abstract
We introduce a new family of symmetric functions, which are $q$analogues of products of Schur functions defined in terms of ribbon tableaux. These functions can be interpreted in terms of the Fock space representation of the quantum affine algebra of type $A_{n1}^{(1)}$ and are related to HallLittlewood functions via the geometry of flag varieties. We present a series of conjectures, and prove them in special cases. The essential step in proving that these functions are actually symmetric consists in the calculation of a basis of highest weight vectors of the $q$Fock space using ribbon tableaux.
 Publication:

eprint arXiv:qalg/9512031
 Pub Date:
 December 1995
 arXiv:
 arXiv:qalg/9512031
 Bibcode:
 1995q.alg....12031L
 Keywords:

 Mathematics  Quantum Algebra
 EPrint:
 35 pages, latex, epic and eepic macros