اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدDemazure Characters and Affine Fusion Rules
73
0
0.0
(
0
)
تأليف
M.A. Walton
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
The Demazure character formula is applied to the Verlinde formula for affine fusion rules. We follow Littelmanns derivation of a generalized Littlewood-Richardson rule from Demazure characters. A combinatorial rule for affine fusions does not result, however. Only a modified version of the Littlewood-Richardson rule is obtained that computes an (old) upper bound on the fusion coefficients of affine $A_r$ algebras. We argue that this is because the characters of simple Lie algebras appear in this treatment, instead of the corresponding affine characters. The Bruhat order on the affine Weyl group must be implicated in any combinatorial rule for affine fusions; the Bruhat order on subgroups of this group (such as the finite Weyl group) does not suffice.
قيم البحث
اقرأ أيضاً
In this paper, we consider how to express an Iwahori--Whittaker function through Demazure characters. Under some interesting combinatorial conditions, we obtain an explicit formula and thereby a generalization of the Casselman--Shalika formula. Under
the same conditions, we compute the transition matrix between two natural bases for the space of Iwahori fixed vectors of an induced representation of a p-adic group; this generalizes a result of Bump--Nakasuji.
We give some higher dimensional analogues of the Durfee square formula and point out their relation to dissections of multipartitions. We apply the results to write certain affine Lie algebra characters in terms of Universal Chiral Partition Functions.
We revisit the study of the multiplets of the conformal algebra in any dimension. The theory of highest weight representations is reviewed in the context of the Bernstein-Gelfand-Gelfand category of modules. The Kazhdan-Lusztig polynomials code the r
elation between the Verma modules and the irreducible modules in the category and are the key to the characters of the conformal multiplets (whether finite dimensional, infinite dimensional, unitary or non-unitary). We discuss the representation theory and review in full generality which representations are unitarizable. The mathematical theory that allows for both the general treatment of characters and the full analysis of unitarity is made accessible. A good understanding of the mathematics of conformal multiplets renders the treatment of all highest weight representations in any dimension uniform, and provides an overarching comprehension of case-by-case results. Unitary highest weight representations and their characters are classified and computed in terms of data associated to cosets of the Weyl group of the conformal algebra. An executive summary is provided, as well as look-up tables up to and including rank four.
This paper studies the properties of Demazure atoms and characters using linear operators and also tableaux-combinatorics. It proves the atom-positivity property of the product of a dominating monomial and an atom, which was an open problem. Furtherm
ore, it provides a combinatorial proof to the key-positivity property of the product of a dominating monomial and a key using skyline fillings, an algebraic proof to the key-positivity property of the product of a Schur function and a key using linear operator and verifies the first open case for the conjecture of key-positivity of the product of two keys using linear operators and polytopes.
This is an expository introduction to fusion rules for affine Kac-Moody algebras, with major focus on the algorithmic aspects of their computation and the relationship with tensor product decompositions. Many explicit examples are included with figur
es illustrating the rank 2 cases. New results relating fusion coefficients to tensor product coefficients are proved, and a conjecture is given which shows that the Frenkel-Zhu affine fusion rule theorem can be seen as a beautiful generalization of the Parasarathy-Ranga Rao-Varadarajan tensor product theorem. Previous work of the author and collaborators on a different approach to fusion rules from elementary group theory is also explained.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
