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Some closed formulas for canonical bases of Fock spaces


Authors: Bernard Leclerc and Hyohe Miyachi
Journal: Represent. Theory 6 (2002), 290-312
MSC (2000): Primary 17B37, 05E05, 05E10, 20C20, 20C33
DOI: https://doi.org/10.1090/S1088-4165-02-00136-X
Published electronically: September 19, 2002
MathSciNet review: 1927956
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Abstract: We give some closed formulas for certain vectors of the canonical bases of the Fock space representation of $U_v(\widehat{\mathfrak{sl}}_n)$. As a result, a combinatorial description of certain parabolic Kazhdan-Lusztig polynomials for affine type $A$ is obtained.


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Additional Information

Bernard Leclerc
Affiliation: Département de Mathématiques, Université de Caen, Campus II, Bld Maréchal Juin, BP 5186, 14032 Caen Cedex, France
Email: leclerc@math.unicaen.fr

Hyohe Miyachi
Affiliation: Department of Mathematics, Graduate School of Science and Technology, Chiba University, Yayoi-cho, Chiba 263-8522, Japan
Address at time of publication: IHES, Le Bois-Marie, 35, route de Chartres, F-91440 Bures-sur-Yvette, France
Email: miyachi@ihes.fr; mihachi_hyohe@ma.noda.tus.ac.jp

DOI: https://doi.org/10.1090/S1088-4165-02-00136-X
Received by editor(s): September 6, 2001
Received by editor(s) in revised form: June 19, 2002
Published electronically: September 19, 2002
Article copyright: © Copyright 2002 American Mathematical Society