Total positivity is a quantum phenomenon : the grassmannian case /

Total positivity is a quantum phenomenon : the grassmannian case /

Saved in:

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.

Mansueto

Loading map link

Holdings details from Mansueto
Call Number:	QA1.A528 no.1448 c.1
c.1	To check availability consult the series record. Intellectual item Need help? - Ask a Librarian