Ribbon tableaux, Hall{endash}Littlewood functions, quantum affine algebras, and unipotent varieties

Journal Article · Sat Feb 01 00:00:00 EST 1997 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.531807· OSTI ID:466881

Lascoux, A ^[1]; Leclerc, B ^[2]; Thibon, J ^[3]

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1. Institut Blaise Pascal, L.I.T.P., Universite Paris 7, 2 place Jussieu, 75251 Paris cedex 05 (France)
2. Universite de Caen, Departement de Mathematiques, Esplanade de la Paix, BP 5186, 14032 Caen cedex (France)
3. Institut Gaspard Monge, Universite de Marne-la-Vallee, 2 rue de la Butte-Verte, 93166 Noisy-le-Grand cedex (France)

We introduce a new family of symmetric functions, which are q analogs of products of Schur functions, defined in terms of ribbon tableaux. These functions can be interpreted in terms of the Fock space representation scr(F){sub q} of U{sub q}(sl{sub n}), and are related to Hall{endash}Littlewood 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 scr(F){sub q} using ribbon tableaux. {copyright} {ital 1997 American Institute of Physics.}

• OSTI ID: 466881
• Journal Information: Journal of Mathematical Physics, Vol. 38, Issue 2; Other Information: PBD: Feb 1997
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
QUANTUM MECHANICS
ANALYTIC FUNCTIONS
SYMMETRY
ALGEBRA
GEOMETRY
VECTORS
WEIGHTING FUNCTIONS