## Coordinate rings and birational charts

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

## Abstract:

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: fomin@umich.edu
**George Lusztig**- Affiliation: Department of Mathematics, M.I.T., Cambridge, Massachusetts 02139
- MR Author ID: 117100
- Email: gyuri@mit.edu
- 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: https://doi.org/10.1090/ert/592
- MathSciNet review: 4359428