Results 11 to 20 of about 593 (37)

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., Mohamad, Mahathir, Okado, Masato   +2 more
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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

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

Singularities of nilpotent Slodowy slices and collapsing levels of W-algebras

Forum of Mathematics, Sigma
We develop techniques to construct isomorphisms between simple affine W-algebras and affine vertex algebras at admissible levels. We then apply these techniques to obtain many new, and conjecturally all, admissible collapsing levels for affine W-algebras.
Tomoyuki Arakawa, Jethro van Ekeren, Anne Moreau   +2 more
doaj   +1 more source

W-algebras at the critical level

, 2011
Let g be a complex simple Lie algebra, f a nilpotent element of g. We show that (1) the center of the W-algebra $W^{cri}(g,f)$ associated with (g,f) at the critical level coincides with the Feigin-Frenkel center of the affine Lie algebra associated with ...
Arakawa, Tomoyuki
core   +1 more source

Smooth locus of twisted affine Schubert varieties and twisted affine Demazure modules

Forum of Mathematics, Sigma
Let ${\mathscr {G}} $ be a special parahoric group scheme of twisted type over the ring of formal power series over $\mathbb {C}$ , excluding the absolutely special case of $A^{(2)}_{2\ell }$ .
Marc Besson, Jiuzu Hong
doaj   +1 more source

A BGG-type resolution for tensor modules over general linear superalgebra

, 2008
We construct a Bernstein-Gelfand-Gelfand type resolution in terms of direct sums of Kac modules for the finite-dimensional irreducible tensor representations of the general linear superalgebra.
A. Berele, A. Rocha-Caridi, A. Rocha-Caridi, A. Sergeev, H. Garland, J. Brundan, J. Lepowsky, Jae-Hoon Kwon, Ngau Lam, S. Kumar, S.-J. Cheng, S.-J. Kang, Shun-Jen Cheng, Y.M. Zou   +13 more
core   +1 more source

On modules for double affine Lie algebras

, 2015
Imaginary Verma modules, parabolic imaginary Verma modules, and Verma modules at level zero for double affine Lie algebras are constructed using three different triangular decompositions.
Jing, Naihuan, Wang, Chunhua
core   +1 more source

Kostka-Foulkes polynomials for symmetrizable Kac-Moody algebras [PDF]

, 2008
We introduce a generalization of the classical Hall-Littlewood and Kostka-Foulkes polynomials to all symmetrizable Kac-Moody algebras. We prove that these Kostka-Foulkes polynomials coincide with the natural generalization of Lusztig's $t$-analog of ...
Viswanath, Sankaran
core   +1 more source

Locally finite admissible simple Lie algebras [PDF]

, 2010
We introduce a class of Lie algebras called admissible Lie algebras. We show that a locally finite admissible simple Lie algebra contains a nonzero maximal toral subalgebra and the corresponding root system is an irreducible locally finite root ...
Yousofzadeh, Malihe
core