Results 131 to 140 of about 340,767 (237)

Zero Action on Perfect Crystals for U_q(G_2^{(1)})

open access: yesSymmetry, Integrability and Geometry: Methods and Applications, 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.
Kailash C. Misra   +2 more
doaj   +1 more source

The PBW Filtration, Demazure Modules and Toroidal Current Algebras

open access: yesSymmetry, Integrability and Geometry: Methods and Applications, 2008
Let L be the basic (level one vacuum) representation of the affine Kac-Moody Lie algebra ^g. The m-th space F_m of the PBW filtration on L is a linear span of vectors of the form x_1dots x_lv_0, where l ≤ m, x_i in ^g and v_0 is a highest weight vector ...
Evgeny Feigin
doaj   +1 more source

The Relationship between Zhedanov's Algebra AW(3) and the Double Affine Hecke Algebra in the Rank One Case

open access: yesSymmetry, Integrability and Geometry: Methods and Applications, 2007
Zhedanov's algebra AW(3) is considered with explicit structure constants such that, in the basic representation, the first generator becomes the second order q-difference operator for the Askey-Wilson polynomials. It is proved that this representation is
Tom H. Koornwinder
doaj  

Affine and Finite Lie Algebras and Integrable Toda Field Equations on Discrete Space-Time

open access: yesSymmetry, Integrability and Geometry: Methods and Applications, 2012
Difference-difference systems are suggested corresponding to the Cartan matrices of any simple or affine Lie algebra. In the cases of the algebras $A_N$, $B_N$, $C_N$, $G_2$, $D_3$, $A_1^{(1)}$, $A_2^{(2)}$, $D^{(2)}_N$ these systems are proved to be ...
Rustem Garifullin   +2 more
doaj   +1 more source

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