Total positivity is a quantum phenomenon : the grassmannian case /

Total positivity is a quantum phenomenon : the grassmannian case /

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Bibliographic Details
Author / Creator:Launois, S., author.
Imprint:Providence, Rhode Island : American Mathematical Society, [2023].
©2023
Description:v, 109 pages : illustrations ; 26 cm
Language:English
Series:Memoirs of the American Mathematical Society 0065-9266 number 1448
Memoirs of the American Mathematical Society ; v. 1448.
Subject:
Grassmann manifolds.
Algebra.
Quantum groups.
Format: Print Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/13414450
Hidden Bibliographic Details
Other authors / contributors:Lenagan, T. H., author.
Nolan, B. M., author
ISBN:1470466945
9781470466947
Notes:"November 2023, volume 291, number 1448 (third of 5 numbers."
Includes bibliographic references.
Summary:"The main aim of this paper is to establish a deep link between the totally nonnegative grassmannian and the quantum grassmannian. More precisely, under the assumption that the deformation parameter q is transcendental, we show that "quantum positroids" are completely prime ideals in the quantum grassmannian Oq(Gmn(F)). As a consequence, we obtain that torus-invariant prime ideals in the quantum grassmannian are generated by polynormal sequences of quantum Plücker coordinates and give a combinatorial description of these generating sets. We also give a topological description of the poset of torus-invariant prime ideals in Oq(Gmn(F)), and prove a version of the orbit method for torus-invariant objects. Finally, we construct separating Ore sets for all torus-invariant primes in Oq(Gmn(F)). The latter is the first step in the Brown-Goodearl strategy to establish the orbit method for (quantum) grassmannians.
Description
Item Description:"November 2023, volume 291, number 1448 (third of 5 numbers."
Physical Description:v, 109 pages : illustrations ; 26 cm
Bibliography:Includes bibliographic references.
ISBN:1470466945
9781470466947
ISSN:0065-9266

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