Research Publications:

• Imaginary crystal bases for $U_q(\widehat{\mathfrak{sl}(2)})$-modules in category $\mathcal O^q_{\text{red,im}}$, Contemp. Math., 713, (2018), 47 - 59,
  (with Cox and Futorny).
  
  
• Kostant-Lusztig $\bA$-bases of Multiparameter Quantum Groups, Contemp. Math., 713, (2018), 149 - 164, (with Jing and Yamane).
  
  
• Affine Geometric Crystal of $A_n^{(1)}$ and Limit Kirrilov-Reshetikhin Perfect Crystals, J. Algebra, 507 (2018), 249 - 291, (with Nakashima).
  
  
• Criteria for solvability and supersolvability in Leibniz Algebras, Commun.in Algebra, 46 (2018), 2083 - 2088, (with Stitzinger and Turner).
  
  
• On realization of some twisted toroidal Lie algebras, Contemp. Math., 695, (2018), 139 - 148, (with N. Jing and C. Mangum).
  
  
• Lattice Paths, Young Tableaux, and Weight Multiplicities, Annals Comb., 22 (2018), 147 - 156, (with R. Jayne)
  
  
• On Classification of Four Dimensional Nilpotent Leibniz Algebras, Commun.in Algebra, 45 (2017), 1012 - 1018, (with Demir and Stitzinger).
  
  
• Imaginary Verma Modules for $U_q(\widehat{sl(2)})$ and Crystal-like bases, J. Algebra, 481 (2017), 12 - 35, (with Cox and Futorny).
  
  
• On principal realization of modules for the affine Lie algebra $A_1 ^{(1)}$ at the critical level, Trans. Amer. Math. Soc. 369 (2017), 5113 - 5136,
  (with Adamovic and Jing).
  
  
• Root Multiplicities of the indefinite Kac-Moody Algebra $HD_n^{(1)}$, Commun. in Algebra, 44, (2016), 1599 - 1614, (with Wilson).
  
  
• Classification of some Solvable Leibniz Algebras, Algebras and Representation Theory, 19 (2016), 405 - 417, (with Demir and Stitzinger).
  
  
• On nilpotent Lie algebras of small breadth, J. Algebra, 444 (2015), 328 - 338 ( with Khuhirun and Stitzinger).
  
  
• Imaginary Verma Modules and Kashiwara Algebras for $U_q(\widehat{g})$, J. Algebra, 424 (2015), 390 - 415
  (with Cox and Futorny).
  
  
• 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., 

•  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 Theory,  14, (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. Algebra,  30, (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
  

• 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. Algebra,  230, (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. B,  510 [PM], (1998), 555-576 (with Kuniba, Okado, Takagi and Uchiyama).

• Crystals for Demazure modules of classical affine Lie algebras, J. Algebra,  208, (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. Algebra,  200, (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,

•  An application of crystal bases to representations of affine Lie algebras,  J. Algebra,  173, (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 $U_q(D^{(2)}_{l+1})$, 

• 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. A,  7,  (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. Algebra,  137, (1991), 56-76.

•  The monoid generated by projections in a Kac-Moody Lie algebra, `Monoids and Semigroups with applications,' (ed. J. Rhodes);

•  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,          
  

•  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

•  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. Algebra,  88, (1984), 196-227.
  

•  Visco-elastic flow due to a plate which starts oscillating in the presence of a parallel stationary plate, Rheologica Acta,  21,

•  Harmonically oscillating visco-elastic boundary layer flow,  Acta Mechanica,  31, (1979) 213-220, (with J. Panda and J. S. Roy).