nLab Boris Feigin

Boris Feigin is a Russian mathematician and mathematical physicist, former student of D. B. Fuks (Fuchs). His works include fundamental contributions to algebraic K-theory, cyclic homology, Lie theory, especially the cohomology of infinite-dimensional Lie algebras, characteristic classes of foliations, representation theory of Virasoro and Kac-Moody Lie algebras and loop groups, semiinfinite cohomology, vertex operator algebras and CFT, geometric Langlands program, quantum groups, deformation theory, integrable systems and algebraic geometry

• dedications to B.F. in a special volume in his honour

• MathGenealogy page

• German Wikipedia entry

Selected writings

On the hypergeometric integral construction of conformal blocks for the $\mathfrak{sl}(n)$ WZW model:

• Boris Feigin, Vadim Schechtman, Alexander Varchenko, On algebraic equations satisfied by correlators in Wess-Zumino-Witten models, Lett Math Phys 20 (1990) 291–297 $[$doi:10.1007/BF00626525$]$

• Boris Feigin, Vadim Schechtman, Alexander Varchenko, On algebraic equations satisfied by hypergeometric correlators in WZW models. I, Commun. Math. Phys. 163 (1994) 173–184 $[$doi:10.1007/BF02101739$]$

  (for $\mathfrak{sl}(2, \mathbb{C})$)

• Boris Feigin, Vadim Schechtman, Alexander Varchenko, On algebraic equations satisfied by hypergeometric correlators in WZW models. II, Comm. Math. Phys. 170 1 (1995) 219-247 $[$euclid:cmp/1104272957$]$

On fractional level WZW models (non-integrable admissible affine Lie algebra irreps) for $\mathfrak{sl}(2, \mathbb{C})$:

• Boris Feigin, Feodor Malikov, Modular functor and representation theory of $\widehat{\mathfrak{sl}_2}$ at a rational level, p. 357-405 in: Loday, Stasheff, Voronov (eds.) Operads: Proceedings of Renaissance Conferences, Contemporary Mathematics 202, AMS (1997) [arXiv:q-alg/9511011, ams:conm-202]

  (appearance of $\mathfrak{osp}(1\vert2)$-contributions)

On KK-compactification of D=6 N=(2,0) SCFT on 4-manifolds to 2d CFTs:

• Boris Feigin, Sergei Gukov, $VOA[M_4]$, J. Math. Phys. 61 012302 (2020) [arXiv:1806.02470, doi:10.1063/1.5100059]

category: people