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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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Some closed formulas for canonical bases of Fock spaces
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by Bernard Leclerc and Hyohe Miyachi PDF
Represent. Theory 6 (2002), 290-312 Request permission


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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Additional 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