Research Publications:

• 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), 21 pages

• 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,
•  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.);
•  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).
•  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).