Results 1 to 10 of about 545 (25)
Beilinson–Drinfeld Schubert varieties and global Demazure modules
Forum of Mathematics, Sigma, 2021 We compute the spaces of sections of powers of the determinant line bundle on the spherical Schubert subvarieties of the Beilinson–Drinfeld affine Grassmannians. The answer is given in terms of global Demazure modules over the current Lie algebra.
Ilya Dumanski +2 more
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Defining relations of quantum symmetric pair coideal subalgebras
Forum of Mathematics, Sigma, 2021 We explicitly determine the defining relations of all quantum symmetric pair coideal subalgebras of quantised enveloping algebras of Kac–Moody type. Our methods are based on star products on noncommutative ${\mathbb N}$-graded algebras.
Stefan Kolb, Milen Yakimov
doaj +1 more source
Remarks on level one conformal blocks divisors [PDF]
, 2013 We show that conformal blocks divisors of type B_r and D_r at level one are effective sums of boundary divisors of $\bar{M}_{0,n}$. We also prove that the conformal blocks divisor of type $B_r$ at level 1 with weights (\omega_1,\dots,\omega_1) scales ...
Mukhopadhyay, Swarnava
core +3 more sources
Lie Superalgebras arising from bosonic representation [PDF]
, 2012 A 2-toroidal Lie superalgebra is constructed using bosonic fields and a ghost field. The superalgebra contains $osp(1|2n)^{(1)}$ as a distinguished subalgebra and behaves similarly to the toroidal Lie superalgebra of type $B(0, n)$.
Jing, Naihuan, Xu, Chongbin
core +1 more source
Demazure Modules, Chari-Venkatesh Modules and Fusion Products [PDF]
, 2014 Let $\mathfrak{g}$ be a finite-dimensional complex simple Lie algebra with highest root $\theta$. Given two non-negative integers $m$, $n$, we prove that the fusion product of $m$ copies of the level one Demazure module $D(1,\theta)$ with $n$ copies of ...
Ravinder, Bhimarthi
core +2 more sources
A construction of some ideals in affine vertex algebras
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 15, Page 971-980, 2003., 2003 We study ideals generated by singular vectors in vertex operator algebras associated with representations of affine Lie algebras of types A and C. We find new explicit formulas for singular vectors in these vertex operator algebras at integer and half‐integer levels.
Dražen AdamoviĆ
wiley +1 more source
Zero Action on Perfect Crystals for U_q(G_2^{(1)}) [PDF]
, 2010 The actions of 0-Kashiwara operators on the $U'_q(G_2^{(1)})$-crystal $B_l$ in [Yamane S., J. Algebra 210 (1998), 440-486] are made explicit by using a similarity technique from that of a $U'_q(D_4^{(3)})$-crystal.
Misra, Kailash C. +2 more
core +3 more sources
ROUQUIER’S CONJECTURE AND DIAGRAMMATIC ALGEBRA
Forum of Mathematics, Sigma, 2017 We prove a conjecture of Rouquier relating the decomposition numbers in category ${\mathcal{O}}$ for a cyclotomic rational Cherednik algebra to Uglov’s ...
BEN WEBSTER
doaj +1 more source
Epsilon Systems on Geometric Crystals of Type $A_n$ [PDF]
, 2010 We introduce an epsilon system on a geometric crystal of type $A_n$, which is a certain set of rational functions with some nice properties. We shall show that it is equipped with a product structure and that it is invariant under the action of tropical ...
Nakashima, Toshiki
core +4 more sources
DJKM algebras I: Their Universal Central Extension
, 2010 The purpose of this paper is to explicitly describe in terms of generators and relations the universal central extension of the infinite dimensional Lie algebra, $\mathfrak g\otimes \mathbb C[t,t^{-1},u|u^2=(t^2-b^2)(t^2-c^2)]$, appearing in the work of ...
Cox, Ben, Futorny, Vyatcheslav
core +1 more source