Research Publications:

• Imaginary Verma Modules and Kashiwara Algebras for $U_q(\widehat{\it {g}})$, J. Algebra,to appear
(with Cox and Futorny) (30 pages).

• An imaginary PBW basis for quantum affine algebras of type 1, J. Pure and Appl. Algebra, 219 (2015), 83 - 100
(with Cox and Futorny).

• Tensor Product Decomposition of $\widehat{sl}(n)$ Modules and Identities, Cont. Math., 627 (2014), 131 -144
(with Wilson).

• On some structures of Leibniz algebras, Cont. Math., 623 (2014), 41 - 54 (with Demir and Stitzinger).

• A note on $U_q(D_4^{(3)})$ - Demazure crystals, Cont. Math., 623 (2014), 13 - 22 (with Armstrong).

• On multiplicities of maximal weights of $\widehat{sl}(n)$-modules, Algebr. Represent. Theory, 17(4) (2014), 1303 - 1321
(with Jayne).

• Realization of $\widehat{sl}_2(\bf{C})$ at the critical level, Comm. Cont. Math., 16(2) (2014) 1450006, (13 pages)
(with Dunbar and Jing).

• On Tensor Product Decomposition of $\widehat{sl}(n)$ modules, J. Alg. and Appl., 12(8) (2013) 1350054, (16 pages)
(with Wilson).

• Soliton Cellular Automaton associated with $D_n^{(1)}-crystal$B^{2,s}$, J. Math. Phys. , 54 (2013) 043301, (33 pages) (with Wilson). •$A_n^{(1)}$-Geometric Crystal Corresponding to Dynkin Index$i=2$and its Ultra-Discretization, in: "Symmetries, Integrable Systems and Representations " , Springer Proceedings in Mathematics and Statistics, volume 40 (2013), 297-318 (with Nakashima). • Ultra-Discretization of the$D_4^{(3)}$-Geometric Crystals to$U_q(G_2^{(1)})$-Perfect Crystals, Pacific J. Math. 255 (2012), 117-142 (with Igarashi and Nakashima). • Soliton Cellular Automaton associated with$U_q(G_2^{(1)})$crystal base, J. Math. Phys. 53 (2012) 013510 (21 pages) (with Okado, Wilson). • Demazure Crystals and Extended Young Diagrams, Algebra Colloquium 19 (2012), 293 - 304 (with Beier). • On Demazure crystals for$U_q(G_2^{(1)})$, Proc. Amer. Math. Soc. 139 (2011), 2343-2356 (with Jayne). • Perfect Crystals for the quantum affine algebra$U_q(C_n^{(1)})$, in: "New Trends in Quantum Integrable Systems", published by World Scientific, (2011), 139 - 156 (with Kang, Kim, Lee). • Zero action on on perfect crystals for$U_q(G_2^{(1)})$, SIGMA, 6 (2010), 022, 12 pages (with Mohamad and Okado). • Imaginary Verma modules and Kashiwara algebras for$U_q(\hat{sl(2)})$, Cont. Math., 506 (2010),105-126 (with Cox and Futorny). • Bosonic Realizations of Toroidal Lie algebras of classical types, Proc. Amer. Math. Soc., 137 (2009), 3609-3618 (with Jing and Xu). • Fermionic Realizations of Toroidal Lie algebras of classical types, J. Algebra, 324 (2010), 183-194 (with Jing). • Root Multiplicities of the indefinite Kac-Moody algebras of symplectic type, Commun. Algebra, 36 (2008), 764-782 (with Klima). • A recurrence relation for characters of highest weight integrable modules for affine Lie algebras, Commun. Cont. Math. 9 (2007), 121-133 (with Cook and Li). • Perfect Crystals of$U_q(D_4^{(3)})$, J. Algebra, 317 (2007), 392-423 (with Kashiwara, Okado and Yamada). • On Demazure crystals for$U_q(D_4^{(3)})$, Cont. Math., 392 (2005), 83-93. • Bosonic realizations of higher level toroidal Lie algebras, Pacific J. Math., 219, (2005) 285-302, (with Jing, Tan). • Combinatorics of quantum affine Lie algebra representations, Cont. Math.343, (2004), 167-189 ,(with Williams). • On the degree of nilpotency of certain subalgebras of Kac-Moody Lie algebras, J. Lie Theory14, (2004), 11-23, (with Kim, Sitzinger). • BRST-resolution for principally graded Wakimoto module of$\widehat{sl}_2$, Lett. Math. Phys., 58, (2002), 181-188 (with Hara, Jing). • On Root Multiplicities of$HA_n^{(1)}$, Int. J. Algebra and Comp.12, (2002), 477-508 (with Hontz). • Root multiplicities of the indefinite Kac-Moody algebras$HD_4^{(3)}$and$HG_2^{(1)}$, Commun. Algebra30, (2002), 2941-2959 (with Hontz). • On multi-color partitions and the generalized Rogers-Ramanujan identities, Commun. Cont. Math. 3, (2001) 533-548 (with Jing and Savage). • The polynomial behavior of weight multiplicities for the affine Kac-Moody algebras$A_r^{(1)}$, Compositio Math.126, (2001), 91-111 (with Benkart, Kang, Lee and Shin). • Paths, Demazure crystals and symmetric functions, J. Math. Phys., 41, (2000), 6477-6486 (with Kuniba, Okado, Takagi and Uchiyama). • q-Wedge modules for quantized enveloping algebras of classical type, J. Algebra230, (2000), 518-539 (with Jing and Okado). • q-vertex operators for quantum affine algebras, Cont. Math., 248, (1999), 293-307 (with Jing). • Level one vertex operator representations of$U_q(C_n^{(1)})$, Sel. Math.,(New series), 5, (1999), 243-255 (with Jing and Koyama). • Vertex operators for twisted quantum affine algebras", Trans. Amer. Math. Soc.351, (1999) 1663-1690, (with Jing). • Characters of Demazure modules and solvable lattice models, Nucl. Phys. B510 [PM], (1998), 555-576 (with Kuniba, Okado, Takagi and Uchiyama). • Crystals for Demazure modules of classical affine Lie algebras, J. Algebra208, (1998), 185-215 (with Kuniba, Okado, Takagi and Uchiyama). • Demazure modules and perfect crystals, Commun. Math. Phys.192, (1998), 555-567 (with Kuniba, Okado and Uchiyama). • Demazure modules and vertex models: the$\widehat{sl}(2)$case, J. Math. Phys.39, (1998), 1601-1622 (with Foda and Okado). • Bosonic realizations of$U_q(C_n^{(1)})$, J. Algebra200, (1998), 155-172 (with Jing and Koyama). • Vertex operators of quantum affine Lie algebras$U_q(B_n^{(1)})$, Letters in Math. Phys.36, (1996), 127-143, (with Jing). • On embedding of integrable highest weight modules of affine Lie algebras, Contemporary Math.193, (1996),287-295. • Weight multiplicity polynomials for affine Kac-Moody algebras of type$A_r^{(1)}$, Compositio Math.104, (1996), 153-187, (with Benkart and Kang). • An application of crystal bases to representations of affine Lie algebras, J. Algebra173, (1995), 436-458, (with Bos). • Indefinite Kac-Moody algebras of special linear type, Pacific J. Math.170 , (1995), 379-404, (with Benkart and Kang). • Level two representations of$A_7^{(2)}$and Rogers-Ramanujanidentities, Commun. Algebra, 22, (1994), 3985-3988, (with Bos). • Crystal bases of Verma modules for quantum affine Lie algebras, Compositio Math.92, (1994), 299-325, (with Kang and Kashiwara). • Indefinite Kac. Moody algebras of classical type, Adv. Math.105, (1994), 76-110, (with Benkart and Kang). • Crystal bases and tensor product decompositions of$U_q(G_2)$-modules, J. Algebra, 163, (1994), 675-691, (with Kang). • Representations of quantum affine Lie algebras and crystal bases, Cont. Math.153, (1993), 79-93 . • Fock space representations of the quantized universal enveloping algebras$U_q(C_l^{(1)}), U_q(A^{(2)}_{2l})$and$U_q(D^{(2)}_{l+1})$, J. Algebra, 155 , (1993), 238-251, (with Kang and Miwa). • Graded Lie algebras of Kac-Moody type, Adv. Math., 97, (1993), 154-190, (with Benkart and Kang). • Perfect crystals of quantum affine Lie algebras, Duke Math. J.68, (1992), 499-607 (with Kang, Kashiwara,Miwa, Nakashima, and Nakayashiki). • Affine crystals and Vertex models, Int. J. Mod. Phys. A7, (1992), 449-484, (with Kang, Kashiwara, Miwa, Nakashima, and Nakayashiki). • Vertex models and crystals, C. R. Acad. Sci. Paris, 315, (1992), 375-380 (with Kang, Kashiwara, Miwa, Nakashima and Nakayashiki). • Projections in Kac-Moody Lie algebras, Proc. Amer. Math. Soc.116, (1992), 351-359, (with Putcha). • Combinatorics of representations of$U_q(\widehat{\it sl}(n))$at$q=0$, Commun. Math. Phys.136, (1991), 543-566, (with Jimbo, Miwa and Okado). • Level two standard$\tilde A_n$-modules, J. Algebra137, (1991), 56-76. • The monoid generated by projections in a Kac-Moody Lie algebra, `Monoids and Semigroups with applications,' (ed. J. Rhodes); World Scientific, (1991), 312-323, (with Putcha). • Crystal base for the basic representation of$U_q(\widehat{s\ell}(n))$, Commun. Math. Phys.134, (1990), 79-88, (with Miwa). • Level one standard modules for affine symplectic Lie algebras, Math. Ann.287, (1990), 287-302. • On irreducible highest weight representations of some affine Lie algebras, Cont. Math., 110, (1990),177-201. • Realization of the level one standard$\tilde C_{2k+1}$-modules, Trans. Amer. Math. Soc.321, (1990), 483-504. • Transitive maps from posets to Dynkin diagrams, J. Pure and Appl. Algebra, 63, (1990), 195-206, (with Putcha and Singh). • Realization of the level two standard${s\ell}(2k+1,\bf C)^\sim$-modules, Trans. Amer. Math. Soc.316, (1989), 295-309. • Specialized characters for affine Lie algebras and the Rogers-Ramanujan identities, Ramanujan Revisited, (eds. G. E.Andrews et al.); Academic Press, (1988), 85-109. • Constructions of fundamental representations of symplectic affine Lie algebras, Topological and Geometrical Methods in Field Theory, (eds. J. Hietarinta and J. Westerholm); World Scientific, (1986), 147-169. • Basic representations of some affine Lie algebras and the generalized Euler identities, J. Australian Math. Soc. (Series A)42, (1987), 296-311. • Standard representations of some affine Lie algebras, Vertex operators in Mathematics and Physics, (eds. J. Lepowsky, S.Mendelstam and I. M. Singer), MSRI, pub. #3, Springer-Verlag (1985),163-183. • Structure of some standard modules for$C_n^1$, J. Algebra, 90, (1984), 385-40. • Structure of the standard modules for$A_n^1\$ and the Rogers-Ramanujan identities,  J. Algebra88, (1984), 196-227.
•  Visco-elastic flow due to a plate which starts oscillating in the presence of a parallel stationary plate, Rheologica Acta,  21,
(1982) 25-29, (with S. P. Mishra).
•  Harmonically oscillating visco-elastic boundary layer flow,  Acta Mechanica,  31, (1979) 213-220, (with J. Panda and J. S. Roy).