Lusztig's positive root vectors and a Dolbeault complex for the A-series full quantum flag manifolds

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10510276" target="_blank" >RIV/00216208:11320/25:10510276 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=wO8WLYzXQM" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=wO8WLYzXQM</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jalgebra.2025.03.035" target="_blank" >10.1016/j.jalgebra.2025.03.035</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Lusztig's positive root vectors and a Dolbeault complex for the A-series full quantum flag manifolds

Popis výsledku v původním jazyce

For the Drinfeld-Jimbo quantum enveloping algebra Uq(sln+1), we show that the span of Lusztig&apos;s positive root vectors, with respect to Littlemann&apos;s nice reduced decompositions of the longest element of the Weyl group Sn+1, form quantum tangent spaces for the full quantum flag manifold Oq(Fn+1). The associated differential calculi are direct q-deformations of the anti-holomorphic Dolbeault complex of the classical full flag manifold Fn+1. As an application we establish a quantum Borel-Weil theorem for Oq(Fn+1), giving a noncommutative differential geometric realisation of all the finite-dimensional type-1 irreducible representations of Uq(sln+1). Restricting this differential calculus to the quantum Grassmannians is shown to reproduce the celebrated Heckenberger-Kolb anti-holomorphic Dolbeault complex. Lusztig&apos;s positive root vectors for non-nice decompositions of the longest element of Sn+1 are examined for low orders, and are exhibited to either not give tangents spaces, or to produce differential calculi of non-classical dimension. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

Název v anglickém jazyce

Lusztig's positive root vectors and a Dolbeault complex for the A-series full quantum flag manifolds

Popis výsledku anglicky

For the Drinfeld-Jimbo quantum enveloping algebra Uq(sln+1), we show that the span of Lusztig&apos;s positive root vectors, with respect to Littlemann&apos;s nice reduced decompositions of the longest element of the Weyl group Sn+1, form quantum tangent spaces for the full quantum flag manifold Oq(Fn+1). The associated differential calculi are direct q-deformations of the anti-holomorphic Dolbeault complex of the classical full flag manifold Fn+1. As an application we establish a quantum Borel-Weil theorem for Oq(Fn+1), giving a noncommutative differential geometric realisation of all the finite-dimensional type-1 irreducible representations of Uq(sln+1). Restricting this differential calculus to the quantum Grassmannians is shown to reproduce the celebrated Heckenberger-Kolb anti-holomorphic Dolbeault complex. Lusztig&apos;s positive root vectors for non-nice decompositions of the longest element of Sn+1 are examined for low orders, and are exhibited to either not give tangents spaces, or to produce differential calculi of non-classical dimension. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA22-00091S" target="_blank" >GA22-00091S: Geometrické struktury, invariance a diferenciální rovnice se vztahem k matematické fyzice</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2025

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Algebra

ISSN

0021-8693

e-ISSN

1090-266X

Svazek periodika

678

Číslo periodika v rámci svazku

September

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

73

Strana od-do

1-73

Kód UT WoS článku

001469326800001

EID výsledku v databázi Scopus

2-s2.0-105002126516