Zobrazeno 1 - 10
of 59
pro vyhledávání: '"Frenkel, Igor B."'
Autor:
Frenkel, Igor B., Kim, Hyun Kyu
We present a three-dimensional geometric construction of the Virasoro-Bott group, which is a central extension of the group of diffeomorphisms of the circle. Our approach is analogous to the well-known construction of a central extension of the loop
Externí odkaz:
http://arxiv.org/abs/2107.11693
Autor:
Frenkel, Igor B., Zeitlin, Anton M.
Publikováno v:
Commun.Math.Phys. 326 (2014) 145-165
We construct the representations of affine sl(2,R) starting from the unitary representations of the loop ax+b-group. Our approach involves a combinatorial analysis of the correlation functions of the generators and renormalization of the appearing di
Externí odkaz:
http://arxiv.org/abs/1210.2135
Autor:
Frenkel, Igor B., Ip, Ivan C. H.
We construct a special principal series representation for the modular double $U_{q\tilde{q}}(g_R)$ of type $A_r$ representing the generators by positive essentially self-adjoint operators satisfying the transcendental relations that also relate $q$
Externí odkaz:
http://arxiv.org/abs/1111.1033
Autor:
Frenkel, Igor B., Zeitlin, Anton M.
Publikováno v:
Journal of Noncommutative Geometry, 7 (2013) 1007-1026
We construct the quantum group $GL_q(2)$ as the semi-infinite cohomology of the tensor product of two braided vertex operator algebras based on the algebra $W_2$ with complementary central charges $c+\bar{c}=28$. The conformal field theory version of
Externí odkaz:
http://arxiv.org/abs/1110.1696
Autor:
Frenkel, Igor B., Kim, Hyun Kyu
Publikováno v:
Duke Math. J. 161, no. 2 (2012), 305-366
We derive the quantum Teichm\"uller space, previously constructed by Kashaev and by Fock and Chekhov, from tensor products of a single canonical representation of the modular double of the quantum plane. We show that the quantum dilogarithm function
Externí odkaz:
http://arxiv.org/abs/1006.3895
Autor:
Duncan, John F. R., Frenkel, Igor B.
Publikováno v:
Commun. Number Theory Phys. 5 (2011) no. 4, 1-128
In 1939 Rademacher derived a conditionally convergent series expression for the elliptic modular invariant, and used this expression- the first Rademacher sum - to verify its modular invariance. By generalizing Rademacher's approach we construct base
Externí odkaz:
http://arxiv.org/abs/0907.4529
Autor:
Frenkel, Igor B., Zeitlin, Anton M.
Publikováno v:
Commun. Math. Phys.297:687-732, 2010
We obtain the quantum group $SL_q(2)$ as semi-infinite cohomology of the Virasoro algebra with values in a tensor product of two braided vertex operator algebras with complementary central charges $c+\bar{c}=26$. Each braided VOA is constructed from
Externí odkaz:
http://arxiv.org/abs/0812.1620
Autor:
Frenkel, Igor B., Styrkas, Konstantin
We identify the algebra of matrix elements of big projective modules in category O with the regular functions on the big Bruhat cell of G. Analogous extensions of the regular representations of the affine Lie and Virasoro algebras yield vertex operat
Externí odkaz:
http://arxiv.org/abs/math/0409117
Autor:
Frenkel, Igor B., Savage, Alistair
Publikováno v:
Inter. Math. Res. Notices, 28 (2003), p. 1521-1547
We relate two apparently different bases in the representations of affine Lie algebras of type A: one arising from statistical mechanics, the other from gauge theory. We show that the two are governed by the same combinatorics and therefore can be vi
Externí odkaz:
http://arxiv.org/abs/math/0211452
Autor:
Frenkel, Igor B., Malikov, Feodor
We use Kazhdan-Lusztig tensoring to, first, describe annihilating ideals of highest weight modules over an affine Lie algebra in terms of the corresponding VOA and, second, to classify tilting functors, an affine analogue of projective functors known
Externí odkaz:
http://arxiv.org/abs/math/9801065