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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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Coordinate rings and birational charts
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by Sergey Fomin and George Lusztig PDF
Represent. Theory 26 (2022), 1-16 Request permission


Let $G$ be a semisimple simply connected complex algebraic group. Let $U$ be the unipotent radical of a Borel subgroup in $G$. We describe the coordinate rings of $U$ (resp., $G/U$, $G$) in terms of two (resp., four, eight) birational charts introduced by Lusztig [Total positivity in reductive groups, Birkhäuser Boston, Boston, MA, 1994; Bull. Inst. Math. Sin. (N.S.) 14 (2019), pp. 403–459] in connection with the study of total positivity.
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Additional Information
  • Sergey Fomin
  • Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
  • MR Author ID: 230455
  • ORCID: 0000-0002-4714-6141
  • Email:
  • George Lusztig
  • Affiliation: Department of Mathematics, M.I.T., Cambridge, Massachusetts 02139
  • MR Author ID: 117100
  • Email:
  • Received by editor(s): February 20, 2021
  • Received by editor(s) in revised form: October 25, 2021
  • Published electronically: January 5, 2022
  • Additional Notes: The first author was supported by NSF grants DMS-1664722, DMS-2054231 and by a Simons Fellowship. The second author was supported by DMS-1855773
  • © Copyright 2022 American Mathematical Society
  • Journal: Represent. Theory 26 (2022), 1-16
  • MSC (2020): Primary 22E46; Secondary 20G20, 14M15
  • DOI:
  • MathSciNet review: 4359428