PUBLICATION

Preprints

64. Crystal base of the negative half of quantum orthosymplectic superalgebra   (with Il-Seung Jang and Akito Uruno), in preparation 

63.  q-deformed Howe duality for orthosymplectic Lie superalgebras (with Jeong Bae) 

      preprint (2025)  arXiv:2506.05959 (32 pages) 

62. Infinite-level Fock spaces, crystal bases, and tensor product of extremal weight modules of type $A_{+\infty}$  (with Soo-Hong Lee)  

      preprint (2025) arXiv:2501.07941  (72 pages)

Published 

61. Unipotent quantum coordinate ring and cominuscule prefundamental representations   (with Il-Seung Jang and Euiyong Park) 

      Journal of Algebra 673 (2025), 260-303.

60. Affine RSK correspondence and crystal of level zero extremal weight modules (with Hyunse Lee)

      Transformation Groups 30 (2025), 331-391. 

59. Crystal bases of parabolic Verma modules over the quantum orthosymplectic superalgebras   (with Il-Seung Jang and Akito Uruno)

     Journal of Algebra 655 (2024), 537-585.

   (special issue dedicated to the memory of Georgia Benkart)

58. Oscillator representations of quantum affine orthosymplectic superalgebras   (with Sin-Myung Lee and Masato Okado)

      Communications in Mathematical Physics (2024) 405:101.

57. Crystal base of the negative half of the quantum superalgebra $U_q(gl(m|n))$  (with Il-Seung Jang and Akito Uruno)

     Journal of Algebra 635 (2023), 300-347.

56. Affinization of $q$-oscillator representations of $U_q(gl_n)$  (with Sin-Myung Lee)

       Letters in Mathematical Physics 113 (2023) 58.

55. Unipotent quantum coordinate ring and prefundamental representations for types $A_n^{(1)}$ and $D_n^{(1)}$   (with Il-Seung Jang and Euiyong Park) 

    International Mathematics Research Notices  2 (2023), 1119-1172.

54. Super duality for quantum affine algebras of type A (with Sin-Myung Lee)

      International Mathematics Research Notices 23 (2022), 18446-18525.

53. Combinatorial Howe duality of symplectic type (with Taehyeok Heo)

      Journal of Algebra 600 (2022), 1-44.

52. Kirillov-Reshetikhin modules over generalized quantum groups of type A  (with Masato Okado) 

       Publications in Research Institute of Mathematical Sciences 57 (2021), 993-1039.

       (special issue on the 70th birthday of Masaki Kashiwara).

51. Higher level q-oscillator modules over $U_q(C_n^{(1)})$, $U_q(C^{(2)}(n+1))$, and $U_q(B^{(1)}(0,n))$  (with Masato Okado) 

      Communications in Mathematical Physics, 385 (2021), 1041-1082.

50. Lusztig data of Kashiwara-Nakashima tableaux in type D  (with Il-Seung Jang) 

      Algebras and Representation Theory, 24 (2021), 959-989.

49. Flagged Littlewood-Richardson tableaux and branching rule for classical groups (with Il-Seung Jang)

       Journal of Combinatorial Theory, Series A (2021), 105419.

48. R-matrix for generalized quantum groups of type A (with Jeongwu Yu)

      Journal of Algebra 566 (2021), 309-341. 

47. Quantum nilpotent subalgebra of classical quantum groups and affine crystals (with Il-Seung Jang) 

      Journal of Combinatorial Theory, Series A. 168 (2019), 219-254.

46. Lakshmibai-Seshadri paths and non-symmetric Cauchy identity  (with Seung-Il Choi) 

      Algebras and Representation Theory 21 (2018), 1381-1394.

45. Crystals and Schur P-positive expansion  (with Seung-il Choi) 

      Electronic Journal of Combinatorics 25(3) (2018), #P3.7, (27 pages).

44. Combinatorial extension of stable branching rules for classical groups

      Transactions of the American Mathematical Society 370 (2018), 6125-6152

43. Lusztig data of Kashiwara-Nakashima tableaux in types B and C 

      Journal of Algebra, 503 (2018), 222-264.

42. A crystal embedding into Lusztig data of type A 

       Journal of Combinatorial Theory, Series A. 154 (2018), 422-443.

41. Character formulae for queer Lie superalgebras and canonical bases of type A/C

      (with Shun-Jen Cheng and Weiqiang Wang)

      Communications in Mathematical Physics 352 (2017), 1091-1119.

40. Kac-Wakimoto character formula for ortho-symplectic Lie superalgebras (with Shun-Jen Cheng)

      Advances in Mathematics 304 (2017), 1296-1329.

39. Finite-dimensional half-integer weight modules over queer Lie superalgebras (with Shun-Jen Cheng) 

      Communications in Mathematical Physics 346 (2016), 945-965.

38. Super duality and crystal bases for quantum orthosymplectic superalgebras II 

      Journal of Algebraic Combinatorics 43 (2016), 553-588.

37. Super duality and crystal bases for quantum orthosymplectic superalgebras

      International Mathematics Research Notices 23 (2015), 12620-12677.

36. Duality on Fock spaces and combinatorial energy functions  (with Euiyong Park)  

       Journal of Combinatorial Theory, Series A. 134 (2015), 121-146.

35. Irreducible characters of Kac-Moody Lie superalgebras (with Shun-Jen Cheng and Weiqiang Wang)   

      Proceedings of the London Mathematical Society (3) 110 (2015), 108-132.

34. Crystal bases of $q$-deformed Kac modules over the quantum superalgebra $U_q(\mathfrak{gl}(m|n))$

      International Mathematical Research Notices (2014), 512-550.

33. $q$-deformed Clifford algebra and level zero fundamental representations of quantum affine algebras

       Journal of Algebra, 399 (2014), 927-947. 

32. RSK correspondence and classically irreducible Kirillov-Reshetikhin crystals

       Journal of Combinatorial Theory Series A. 120 (2013), 433-452.

31. Littlewood identity and crystal bases

       Advances in Mathematics  230 (2012), 699-745.

30. A plactic algebra for extremal weight crystals and the Cauchy identity for Schur operators

       Journal of Algebraic Combinatorics 34 (2011), 427-449.

29. Crystal bases of modified quantum groups and a double RSK correspondence

       Journal of Combinatorial Theory Series A. 118 (2011), 2131-2156.

28. Crystal duality and Littlewood-Richardson rule of extremal weight crystals

       Journal of Algebra 336 (2011), 99-138.

27. Littlewood-Richardson coefficients and extremal weight crystals

       RIMS Kokyuroku 1689 (2010), 50-60. 

26. Kostant homology formula for oscillator representations of Lie superalgebras

       (with Shun-Jen Cheng and Weiqiang Wang) 

       Advances in Mathematics 224 (2010), 1548-1588.

25. Differential operators and crystal bases of extremal weight modules

       Advances in Mathematics 222 (2009), 1339-1369.

24. Demazure crystals of generalized Verma modules and a flagged RSK correspondence

       Journal of Algebra 322 (2009), 2150-2179.

23. Crystal graphs for general linear Lie superalgebras and quasi-symmetric functions

       Journal of Combinatorial Theory Series A 116 (2009), 1199-1218.

22. Crystal graphs and the combinatorics of Young tableaux

       Handbook of Algebra, vol. 6, 473-504 (Elsevier, 2009).

21. A combinatorial proof of a Weyl type formula for hook Schur polynomials

       Journal of Algebraic Combinatorics, 28 (2008),  439-459.

20. Kostant's homology formulas for infinite-dimensional Lie superalgebras (with Shun-Jen Cheng)

       International Mathematical Research Notices, (2008).

19. Fock space representations of quantum affine algebras and generalized Lascoux-Leclerc-Thibon algorithm

       (with Seok-Jin Kang)   

       Journal of the Korean Mathematical Society, 45 (2008), 1135-1202.

18. A BGG-type resolution for irreducible tensor $\frak{gl}_{m|n}$-modules  (with Shun-Jen Cheng and Ngau Lam) 

      Letters in Mathematical Physics, 85 (2008), 75-87.

17. Rational semistandard tableaux and character formula for the Lie superalgebra $\widehat{frak{gl}}_{\infty|\infty}$

      Advances in Mathematics 217 (2008), 713-739.

16. Crystal graphs for Lie superalgebras and Cauchy decompositions

      Journal of Algebraic Combinatorics, 25 (2007), 57-100.

15. Decomposition of the Fock Space in two-dimensional square lattice systems

      (with Myung-Hoon Chung and Byung-Bae Kim) 

      Letters in Mathematical  Physics, 78 (2006), 73-88.

14. Weight multiplicities for affine Lie algebras of type $A_r^{(1)}$ and Kostka numbers (with Young-Tak Oh)  

      Journal of Algebra  299 (2006), 226-244.

13. Affine crystal graphs and two-colored partitions

      Letters in Mathematical  Physics, 75 (2006), 171-186.

12. Free Lie superalgebras and representations of $\frak{gl}(m,n)$ and $\frak{q}(n)$

      Journal of the Korean Mathematical Society,  42 (2005), 365-386.

11. Crystal bases of the Fock space representations and the string functions  (with Seok-Jin Kang)

       Journal of Algebra  280 (2004), 313-349.

10. Automorphisms of Borcherds superalgebras and fixed point subalgebras

       Journal of Algebra 259 (2003), 533-571.

9. Fock space representations for the quantum affine algebra of type $C_2^{(1)}$  (with Seok-Jin Kang)

     Contemporary Mathematics 325 (2003), 109-131.

8. Reduction of the Hilbert space in strongly correlated systems (with Myung-Hoon Chung) 

     Journal of Mathematical Physics 43 (2002), 4582-4591.

7. Quantum affine algebras, combinatorics of Young Walls and global bases  (with Seok-Jin Kang) 

     Electronic Research Announcements of American Mathematical Society 8 (2002), 35-46.

6. Tensor product of crystal bases over $U_q(\frak{gl}(m,n))$  (with Seok-Jin Kang)

     Communications in Mathematical Physics 224, (2001), 705-732.

5. Peterson-type dimension formulas for graded Lie superalgebras  (with Seok-Jin Kang, Young Tak Oh)  

    Nagoya Mathematical Journal 163 (2001), 107-144.

4. Graded Lie superalgebras, supertrace formula, and orbit Lie superalgebras (with Seok-Jin Kang) 

    Proceedings of London Mathematical Society (3)  81 (2000),   675-724.

3. Decomposition of free Lie algebras into irreducible components  (with Jin Hong) 

     Journal of Algebra 197 (1997), 127-145.

2. Integral points on hyperbolas  (with Jin Hong, Kyeonghoon Jeong)  

    Journal of the Korean Mathematical Society, 34 (1997), no. 1, 149-157.

1. Symmetries of Yoshioka-Halperlin-Lee Hamiltonian for the fractional quantum Hall effect 

    (with Myung-Hoon Chung, Jin Hong)  

    Physics Review B  55 (1997), 2249-2273.