研 究 内 容

無限次元リー代数と量子群の表現論を中心に,可積分系,特殊函数論,組合せ論, 有限次元代数の表現論,幾何学的表現論,D-加群の理論などに興味を持っています.


Research papers & Preprints

  1. PBW basis of quantized universal enveloping algebras, Publ. RIMS 30, no.2 (1994), 209-232.
  2. Geometric construction of crystal bases (with M. Kashiwara), Duke Math. J. 89, no.1 (1997), 9-36.
  3. Quantum toroidal algebras and their vertex representations, Publ. RIMS 34, no. 2 (1998), 155-177.
  4. Toroidal actions on level $1$ modules of $U_q(\widehat{sl}_n)$ (with K. Takemura and D. Uglov), Transformation Groups 3, no. 1 (1998), 75-102.
  5. Hirota bilinear forms with 2-toroidal symmetries (with K. Iohara and M. Wakimoto), Physics Letter A 254, no. 1-2 (1999), 37-46.
  6. Notes on differential equations arising from a representation of 2-toroidal Lie algebras (with K. Iohara and M. Wakimoto), Progr. Theor. Phys. Suppl, No. 135 (1999), 166-181.
  7. Crystal bases and quiver varieties, Math. Ann. 324 (2002), no. 4, 675-688.
  8. Double affine Hecke algebras and elliptic Hecke algberas (with M. Shiota), Progress in Math 284, Representation Theory of Algebraic Groups and Quantum Groups (2010), 297-312.
  9. On Hecke algebras associated with elliptic root systems and the double affine Hecke algebras (with M. Shiota), Publ. RIMS 45 (2009), 845-905.
  10. The rational qKZ equation and shifted non-symmetric Jack polynomials (with S. Kakei, M. Nishizawa and Y. Takeyama), SIGMA 5 (2009), Paper 010, 12 pp.
  11. Indecomposable decomposition of tensor products of modules over the restricted quantum universal enveloping algebra associated to $\boldsymbol{\mathfrak{sl}_2}$ (with H. Kondo), J. Alg. 330 (2011), 103-129.
  12. Toward Berenstein-Zelevinsky data in affine type $A$, I: Construction of affine analogs (with S. Naito and D. Sagaki), Contemp. Math. 565 (2012), 143-184.
  13. Mirkovi\'c Vilonen polytopes and a quiver construction of crystal basis in type $A$, Int. Math. Res. Not. IMRN 2012, no. 17, 3877-3928.
  14. Toward Berenstein-Zelevinsky data in affine type $A$, II: Expicit description (with S. Naito and D. Sagaki), Contemp. Math. 565 (2012), 185-216.
  15. Toward Berenstein-Zelevinsky data in affine type $A$, III: Proof of the connectedness (with S. Naito and D. Sagaki), Symmetries, Integrable Systems and Representations, (2012), 361-402.

Review articles

  1. An introduction to canonical bases, Representations of finite dimensional algebras and related topics in Lie theory and geometry, Fields Inst. Commun., 40 (2004), 431-451.

Talks


その他


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