Commutative Vertex Algebras and Their Degenerations
Funkcionalʹnyj analiz i ego priloženiâ, Tome 48 (2014) no. 3, pp. 24-33.

Voir la notice de l'article provenant de la source Math-Net.Ru

Commutative vertex algebras arising as subalgebras of the vertex algebras corresponding to the Kac–Moody algebras are studied. Systems of defining relations and degenerations into algebras with quadratic relations are described. The results can be used to obtain fermionic formulas for characters.
Mots-clés : vertex algebras
Keywords: Abelianization, quadratic algebras.
@article{FAA_2014_48_3_a2,
     author = {B. L. Feigin},
     title = {Commutative {Vertex} {Algebras} and {Their} {Degenerations}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {24--33},
     publisher = {mathdoc},
     volume = {48},
     number = {3},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2014_48_3_a2/}
}
TY  - JOUR
AU  - B. L. Feigin
TI  - Commutative Vertex Algebras and Their Degenerations
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 2014
SP  - 24
EP  - 33
VL  - 48
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FAA_2014_48_3_a2/
LA  - ru
ID  - FAA_2014_48_3_a2
ER  - 
%0 Journal Article
%A B. L. Feigin
%T Commutative Vertex Algebras and Their Degenerations
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 2014
%P 24-33
%V 48
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FAA_2014_48_3_a2/
%G ru
%F FAA_2014_48_3_a2
B. L. Feigin. Commutative Vertex Algebras and Their Degenerations. Funkcionalʹnyj analiz i ego priloženiâ, Tome 48 (2014) no. 3, pp. 24-33. http://geodesic.mathdoc.fr/item/FAA_2014_48_3_a2/

[1] B. L. Feigin, E. B. Feigin, “Integriruemye $\widehat{sl_2}$-moduli kak beskonechnye tenzornye proizvedeniya”, Fundamentalnaya matematika segodnya, NMU, M., 2003, 304–334 | MR

[2] B. Feigin, A. Stoyanovski, Quasi-particles models for the representations of Lie algebras and geometry of flag manifold, arXiv: hep-th/9308079

[3] A. V. Stoyanovskii, B. L. Feigin,, “Funktsionalnye modeli predstavlenii algebr tokov i polubeskonechnye kletki Shuberta”, Funkts. analiz i ego pril., 28:1 (1994), 68–90 | MR | Zbl

[4] B. Feigin, E. Frenkel, “Coinvariants of nilpotent subalgebras of the Virasoro algebra and partition identities”, I. M. Gelfand Seminar, Adv. Soviet Math., 16, Part 1, Amer. Math. Soc., Providence, RI, 1993, 139–148 | MR | Zbl

[5] B. Feigin, S. Loktev, “On generalized Kostka polynomials and the quantum Verlinde rule”, Differential Topology, Infinite-Dimensional Lie Algebras, and Applications, Amer. Math. Soc. Transl. Ser. 2, 194, Amer. Math. Soc., Providence, RI, 1999, 61–79, arXiv: math/9812093 | MR | Zbl

[6] I. B. Frenkel, V. G. Kac, “Basic representations of affine Lie algebras and dual resonance models”, Invent. Math., 62:1 (1980), 23–66 | DOI | MR | Zbl

[7] B. L. Feigin, M. Jimbo, T. Miwa, E. Mukhin, Y. Takeyama, “Fermionic formulas for $(k,3)$-admissible configurations”, Publ. Res. Inst. Math. Sci., 40:1 (2004), 125–162 | DOI | MR | Zbl

[8] V. Kac, Vertex Algebras for Beginners, University Lecture Series, 10, Amer. Math. Soc., Providence, RI, 1998 | DOI | MR | Zbl