Zero Action on Perfect Crystals for U_q(G_2^{(1)}) (2009)
Misra, Kailash C., Mohamad, Mahathir, Okado, Masato
The explicit zero action of Kashiwara operators on the U'_q(G_2^{(1)})-crystal B_l constructed by Yamane are presented by using a similarity technique from that of a U'_q(D_4^{(3)})-crystal. It is...
Imaginary Verma modules and Kashiwara algebras for $U_q(\widehat{\mathfrak{sl}(2)})$ (2009)
Cox, Ben, Futorny, Vyacheslav, Misra, Kailash C.
We consider imaginary Verma modules for quantum affine algebra $U_q(\hat{\mathfrak{sl}(2)})$ and construct Kashiwara type operators and the Kashiwara algebra $\mathcal K_q$. We show that a certain...
Fermionic realization of toroidal Lie algebras of types ABD (2008)
Jing, Naihuan, Misra, Kailash C.
We use fermionic operators to construct toroidal Lie algebras of types $A_n, B_n$ and $D_n$
Atsuo Kuniba, Kailash C. Misra, Masato Okado, Taichiro Takagi
We review the path realization of Demazure crystals and discuss Demazure characters in the light of symmetric functions. 1
Naihuan Jing, Carla D. Savage, Kailash C. Misra
Basil Gordon, in the sixties, and George Andrews, in the seventies, generalized the Rogers-Ramanujan identities to higher moduli. These identities arise in many areas of mathematics and mathematical...
Perfect Crystals for U_q(D_4^{(3)}) (2006)
Kashiwara, Masaki, Misra, Kailash C., Okado, Masato, Yamada, Daisuke
A perfect crystal of any level is constructed for the Kirillov-Reshetikhin module of $U_q(D_4^{(3)})$ corresponding to the middle vertex of the Dynkin diagram. The actions of Kashiwara operators are...
Cook, William J., Li, Haisheng, Misra, Kailash C.
Using certain results for the vertex operator algebras associated with affine Lie algebras we obtain recurrence relations for the characters of integrable highest weight irreducible modules for an...
Naihuan Jing, Carla D. Savage, Kailash C. Misra
Basil Gordon, in the sixties, and George Andrews, in the seventies, generalized the Rogers-Ramanujan identities to higher moduli. These identities arise in many areas of mathematics and mathematical...
q-Vertex operators for quantum affine algebras (1999)
Jing, Naihuan, Misra, Kailash C.
$q$-vertex operators for quantum affine algebras have played important role in the theory of solvable lattice models and the quantum Knizhnik-Zamolodchikov equation. Explicit constructions of these...
On multi-color partitions and the generalized Rogers-Ramanujan identities (1999)
Naihuan Jing, Kailash C. Misra, Carla D. Savage
Basil Gordon, in the sixties, and George Andrews, in the seventies, generalized the Rogers-Ramanujan identities to higher moduli. These identities arise in many areas of mathematics and mathematical...
$q$-Wedge Modules for Quantized Enveloping Algebras of Classical Type (1998)
Jing, Naihuan, Misra, Kailash C., Okado, Masato
We use the fusion construction in the twisted quantum affine algebras to obtain a unified method to deform the wedge product for classical Lie algebras. As a byproduct we uniformly realize all...
Benkart, Georgia, Kang, Seok-Jin, Lee, Hyeonmi, Misra, Kailash C., Shin, Dong-Uy
We prove that the multiplicity of an arbitrary dominant weight for an integrable highest weight representation of the affine Kac-Moody algebra $A_{r}^{(1)}$ is a polynomial in the rank $r$. In the...
Vertex operators for twisted quantum affine algebras (1997)
Jing, Naihuan, Misra, Kailash C.
We construct explicitly the $q$-vertex operators (intertwining operators) for the level one modules $V(\Lambda_i)$ of the classical quantum affine algebras of twisted types using interacting bosons,...
Bosonic Realizations of $U_q(C^{(1)}_n)$ (1997)
Jing, Naihuan, Koyama, Yoshitaka, Misra, Kailash C.
We construct explicitly the quantum symplectic affine algebra $U_q(\widehat{sp}_{2n})$ using bosonic fields. The Fock space decomposes into irreducible modules of level -1/2, quantizing the...
Demazure Modules and Perfect Crystals (1996)
Kuniba, Atsuo, Misra, Kailash C., Okado, Masato, Uchiyama, Jun
We give a criterion for the Demazure crystal $B_w(\lambda)$ defined by Kashiwara to have a tensor product structure. We study the $\sln$ symmetric tensor case, and see some Demazure characters are...
Demazure modules and vertex models: the affine sl(2) case (1996)
Foda, Omar, Misra, Kailash C., Okado, Masato
We characterize, in the case of affine sl(2), the crystal base of the Demazure module E_w(\La) in terms of extended Young diagrams or paths for any dominant integral weight \La and Weyl group element...