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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

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Some closed formulas for canonical bases of Fock spaces
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by Bernard Leclerc and Hyohe Miyachi
Represent. Theory 6 (2002), 290-312
Published electronically: September 19, 2002


We give some closed formulas for certain vectors of the canonical bases of the Fock space representation of $U_v(\mathfrak {sl}_n)$. As a result, a combinatorial description of certain parabolic Kazhdan-Lusztig polynomials for affine type $A$ is obtained.
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Bibliographic Information
  • Bernard Leclerc
  • Affiliation: Département de Mathématiques, Université de Caen, Campus II, Bld Maréchal Juin, BP 5186, 14032 Caen Cedex, France
  • MR Author ID: 327337
  • Email:
  • 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
  • MR Author ID: 649846
  • Email:;
  • Received by editor(s): September 6, 2001
  • Received by editor(s) in revised form: June 19, 2002
  • Published electronically: September 19, 2002
  • © Copyright 2002 American Mathematical Society
  • Journal: Represent. Theory 6 (2002), 290-312
  • MSC (2000): Primary 17B37, 05E05, 05E10, 20C20, 20C33
  • DOI:
  • MathSciNet review: 1927956