|
SIGMA, 2014, том 10, 032, 16 стр.
(Mi sigma897)
|
|
|
|
Эта публикация цитируется в 7 научных статьях (всего в 7 статьях)
Modules with Demazure Flags and Character Formulae
Vyjayanthi Chari, Lisa Schneider, Peri Shereen, Jeffrey Wand Department of Mathematics, University of California, Riverside, CA 92521, USA
Аннотация:
In this paper we study a family of finite-dimensional graded representations of the current algebra of $\mathfrak{sl}_2$ which are indexed by partitions. We show that these representations admit a flag where the successive quotients are Demazure modules which occur in a level $\ell$-integrable module for $A_1^1$ as long as $\ell$ is large. We associate to each partition and to each $\ell$ an edge-labeled directed graph which allows us to describe in a combinatorial way the graded multiplicity of a given level $\ell$-Demazure module in the filtration. In the special case of the partition $1^s$ and $\ell=2$, we give a closed formula for the graded multiplicity of level two Demazure modules in a level one Demazure module. As an application, we use our result along with the results of Naoi and Lenart et al., to give the character of a $\mathfrak{g}$-stable level one Demazure module associated to $B_n^1$ as an explicit combination of suitably specialized Macdonald polynomials. In the case of $\mathfrak{sl}_2$, we also study the filtration of the level two Demazure module by level three Demazure modules and compute the numerical filtration multiplicities and show that the graded multiplicites are related to (variants of) partial theta series.
Ключевые слова:
Demazure flags; Demazure modules; theta series.
DOI:
https://doi.org/10.3842/SIGMA.2014.032
Полный текст:
PDF файл (434 kB)
Полный текст:
http://emis.mi.ras.ru/journals/SIGMA/2014/032/
Список литературы:
PDF файл
HTML файл
Реферативные базы данных:
ArXiv:
1310.5191
Тип публикации:
Статья
MSC: 06B15 ; 05E10; 14H42 Поступила: 22 октября 2013 г.; в окончательном варианте 17 марта 2014 г.; опубликована 27 марта 2014 г.
Язык публикации: английский
Образец цитирования:
Vyjayanthi Chari, Lisa Schneider, Peri Shereen, Jeffrey Wand, “Modules with Demazure Flags and Character Formulae”, SIGMA, 10 (2014), 032, 16 pp.
Цитирование в формате AMSBIB
\RBibitem{ChaSchShe14}
\by Vyjayanthi~Chari, Lisa~Schneider, Peri~Shereen, Jeffrey~Wand
\paper Modules with Demazure Flags and Character Formulae
\jour SIGMA
\yr 2014
\vol 10
\papernumber 032
\totalpages 16
\mathnet{http://mi.mathnet.ru/sigma897}
\crossref{https://doi.org/10.3842/SIGMA.2014.032}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3210603}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000334686800001}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84897478446}
Образцы ссылок на эту страницу:
http://mi.mathnet.ru/sigma897 http://mi.mathnet.ru/rus/sigma/v10/p32
Citing articles on Google Scholar:
Russian citations,
English citations
Related articles on Google Scholar:
Russian articles,
English articles
Эта публикация цитируется в следующих статьяx:
-
Biswal R., Chari V., Schneider L., Viswanath S., “Demazure Flags, Chebyshev Polynomials, Partial and Mock Theta Functions”, J. Comb. Theory Ser. A, 140 (2016), 38–75
-
C. Lenart, S. Naito, D. Sagaki, A. Schilling, M. Shimozono, “Affine crystals, Macdonald polynomials and combinatorial models extended abstract”, Rev. Roum. Math. Pures Appl., 62:1 (2017), 113–135
-
C. Lenart, S. Naito, D. Sagaki, A. Schilling, M. Shimozono, “A uniform model for Kirillov–Reshetikhin crystals II. Alcove model, path model, and $P = X$”, Int. Math. Res. Notices, 2017, no. 14, 4259–4319
-
D. Jakelic, A. Moura, “Limits of multiplicities in excellent filtrations and tensor product decompositions for affine Kac–Moody algebras”, Algebr. Represent. Theory, 21:1 (2018), 239–258
-
D. Kus, “Representations of Lie superalgebras with fusion flags”, Int. Math. Res. Notices, 2018, no. 17, 5455–5485
-
R. Biswal, V. Chari, D. Kus, “Demazure flags, $q$-Fibonacci polynomials and hypergeometric series”, Res. Math. Sci., 5 (2018), 12
-
Fourier G., Martins V., Moura A., “On Truncated Weyl Modules”, Commun. Algebr., 47:3 (2019), 1125–1146
|
Просмотров: |
Эта страница: | 182 | Полный текст: | 26 | Литература: | 28 |
|