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Mosc. Math. J., 2002, Volume 2, Number 3, Pages 567–588 (Mi mmj64)  

This article is cited in 26 scientific papers (total in 26 papers)

$q$-characters of the tensor products in $\mathbf{sl}_2$-case

B. L. Feigina, E. B. Feiginb

a L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences
b Independent University of Moscow

Abstract: Let $\pi,…,\pi_n$ be irreducible finite-dimensional $\mathbf{sl}_2$-modules. Using the theory of representations of current algebras, we introduce several ways to construct a $q$-grading on $\pi_1\otimes…\otimes\pi_n$. We study the corresponding graded modules and prove that they are essentially the same.

Key words and phrases: Universal enveloping algebra, representation theory, current algebra, Gordon's formula.

DOI: https://doi.org/10.17323/1609-4514-2002-2-3-567-588

Full text: http://www.ams.org/.../abst2-3-2002.html
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Bibliographic databases:

MSC: Primary 05A30; Secondary 17B35
Received: April 14, 2002
Language:

Citation: B. L. Feigin, E. B. Feigin, “$q$-characters of the tensor products in $\mathbf{sl}_2$-case”, Mosc. Math. J., 2:3 (2002), 567–588

Citation in format AMSBIB
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\by B.~L.~Feigin, E.~B.~Feigin
\paper $q$-characters of the tensor products in $\mathbf{sl}_2$-case
\jour Mosc. Math.~J.
\yr 2002
\vol 2
\issue 3
\pages 567--588
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\crossref{https://doi.org/10.17323/1609-4514-2002-2-3-567-588}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1988973}
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    This publication is cited in the following articles:
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    2. Feigin B., Feigin E., “Schubert varieties and the fusion products”, Publ. Res. Inst. Math. Sci., 40:3 (2004), 625–668  crossref  mathscinet  zmath  isi
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    13. S. Loktev, “Weight multiplicity polynomials of multi-variable Weyl modules”, Mosc. Math. J., 10:1 (2010), 215–229  mathnet  mathscinet
    14. Kousidis S., “Asymptotics of Generalized Galois Numbers via Affine Kac-Moody Algebras”, Proc. Amer. Math. Soc., 141:10 (2013), 3313–3326  crossref  mathscinet  zmath  isi  elib
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    16. Ghislain Fourier, “New homogeneous ideals for current algebras: filtrations, fusion products and Pieri rules”, Mosc. Math. J., 15:1 (2015), 49–72  mathnet  mathscinet
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    18. Venkatesh R., “Fusion Product Structure of Demazure Modules”, Algebr. Represent. Theory, 18:2 (2015), 307–321  crossref  mathscinet  zmath  isi
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    20. Chari V., Venkatesh R., “Demazure Modules, Fusion Products and Q-Systems”, Commun. Math. Phys., 333:2 (2015), 799–830  crossref  mathscinet  zmath  isi
    21. Kus D., Venkatesh R., “Twisted Demazure Modules, Fusion Product Decomposition and Twisted Q-Systems”, Represent. Theory, 20 (2016), 94–127  crossref  mathscinet  zmath  isi
    22. Chari V., Shereen P., Venkatesh R., Wand J., “a Steinberg Type Decomposition Theorem For Higher Level Demazure Modules”, J. Algebra, 455 (2016), 314–346  crossref  mathscinet  zmath  isi
    23. Brito M., Pereira F., “Graded Limits of Simple Tensor Product of Kirillov–Reshetikhin Modules For Uq(N+1)”, Commun. Algebr., 44:10 (2016), 4504–4518  crossref  mathscinet  zmath  isi
    24. Naoi K., “Tensor Products of Kirillov-Reshetikhin Modules and Fusion Products”, Int. Math. Res. Notices, 2017, no. 18, 5667–5709  crossref  isi  scopus
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    26. Brito M., Chari V., Moura A., “Demazure Modules of Level Two and Prime Representations of Quantum Affine Sln+1”, J. Inst. Math. Jussieu, 17:1 (2018), 75–105  crossref  mathscinet  zmath  isi  scopus
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