Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/prv-for-the-fusion-product-the-case-documentclass-12pt-minimal-DGIZowNmTm
References (21)
-
P. Cohn (1977)
GROUPES ET ALGÉBRES DE LIE -
A. Beauville (1994)
Conformal blocks, fusion rules and the Verlinde formulaarXiv: Algebraic Geometry
-
Shrawan Kumar (1988)
Proof of the Parthasarathy-Ranga Rao-Varadarajan conjectureInventiones mathematicae, 93
-
K. Parthasarathy, R. Rao, V. Varadarajan (1967)
Representations of Complex Semi-Simple Lie Groups and Lie AlgebrasAnnals of Mathematics, 85
-
(1996)
Conformal blocks -
(1981)
Groupes et Algèbres de Lie, Chap. 4–6 -
P. Belkale (2003)
Quantum generalization of the Horn conjectureJournal of the American Mathematical Society, 21
-
C. Teleman (1995)
Lie algebra cohomology and the fusion rulesCommunications in Mathematical Physics, 173
-
J. Humphreys (1973)
Introduction to Lie Algebras and Representation Theory -
(1994)
A proof for the Verlinde formula -
10.1007/978-93-86279-56-9_5
-
Y. Shimizu, K. Ueno (2001)
Advances in Moduli Theory -
A Tsuchiya (1989)
10.2969/aspm/01910459Adv. Stud. Pure Math., 19
-
O. Mathieu (1988)
Construction du groupe de Kac-Moody et applicationsInternational Journal of Computer Mathematics
-
10.1201/9781003072393-20
-
A. Boysal, Shrawan Kumar (2008)
A conjectural presentation of fusion algebrasarXiv: Group Theory
-
V. Kac (1983)
Infinite Dimensional Lie Algebras -
A. Tsuchiya, K. Ueno, Y. Yamada (1989)
Conformal Field Theory on Universal Family of Stable Curves with Gauge Symmetries, 19
-
K. Parthasarathy, R. Rao, V. Varadarajan (1966)
Representations of complex semisimple Lie groups and Lie algebrasBulletin of the American Mathematical Society, 72
-
Shrawan Kumar (1989)
A refinement of the PRV conjectureInventiones mathematicae, 97
-
(1989)
Construction d'un groupe de Kac-Moody et applications, Compositio Math
- Publisher
- Springer Journals
- Copyright
- Copyright © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021
- ISSN
- 0025-5874
- eISSN
- 1432-1823
- DOI
- 10.1007/s00209-021-02754-2
- Publisher site
- See Article on Publisher Site
Abstract
Given a complex simple Lie algebra g\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\mathfrak g$$\end{document} and a positive integer ℓ\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\ell $$\end{document}, under the assumption λ≫μ\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\uplambda \gg \mu $$\end{document}, we show that irreducible representations of g\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\mathfrak g$$\end{document} of the form V(λ+wμ)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$V(\uplambda +w\mu )$$\end{document}, w∈W,\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$w\in W,$$\end{document} with level at most ℓ\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\ell $$\end{document} appear in the fusion product of V(λ)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$V(\uplambda )$$\end{document} and V(μ)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$V(\mu )$$\end{document}. This verifies the existence of PRV components for the fusion product in this special case.
Journal
Mathematische Zeitschrift – Springer Journals
Published: Dec 1, 2021
Keywords: PRV components; PRV weights; Fusion product; Fusion ring; Primary 20G05; 22E65; 17B10