representations of affine algebras, representations of vertex-operator algebras, conformal field theories, spaces of conformal blocks.
Main publications:
B. L. Feigin, S. A. Loktev, I. Yu. Tipunin, Coinvariants for Lattice VOAs and q-Supernomial Coefficients // Comm. Math. Phys., to appear.
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 (1999), 61–79.
B. Feigin, R. Kedem, S. Loktev, T. Miwa, E. Mukhin. Combinatorics of the $\widehat{sl_2}$ spaces of coinvariants // Transformation Groups, V. 6, no. 1 (2001), 25–52.
B. L. Feigin, S. A. Loktev, I. Yu. Tipunin. Coinvariants for Lattice VOAs and q-Supernomial Coefficients, math.QA/0107003, ITEP-TH-69/01.
S. A. Loktev, B. L. Feigin, “On the Finitization of the Gordon Identities”, Funktsional. Anal. i Prilozhen., 35:1 (2001), 53–61; Funct. Anal. Appl., 35:1 (2001), 44–51
S. A. Loktev, “Fermionic character formulae for representations of $\widehat{sl}_2$”, Uspekhi Mat. Nauk, 56:1(337) (2001), 153–154; Russian Math. Surveys, 56:1 (2001), 164–165
S. A. Loktev, B. L. Feigin, “Cohomology of Nilpotent Subalgebras of the Algebra $\widehat{sl_2}$”, Funktsional. Anal. i Prilozhen., 30:4 (1996), 80–83; Funct. Anal. Appl., 30:4 (1996), 285–287
2015
6.
P. Etingof, S. Loktev, L. Rybnikov, S. Gusein-Zade, Yu. Ilyashenko, S. Lando, M. Tsfasman, V. Vassiliev, “Boris Feigin”, Mosc. Math. J., 15:2 (2015), 185–186
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