WELCOME to Katsuyuki Naoi's Home Page

Japanese English


Katsuyuki NAOI

Associate professor
Institute of Engineering, Tokyo University of Agriculture and Technology
2-24-16 Naka-cho, Koganei-shi, Tokyo 184-8588, JAPAN
naoik_at_cc.jskrtf.com


Contents

Papers and Preprints

  1. Strong duality Data of type A and extended T-systems, Transformation Groups (2024), 47 pages (Open Access), arXiv:2305.15681.
  2. Equivalence between module categories over quiver Hecke algebras and Hernandez-Leclerc's categories in general types, Advances in Mathematics 389 (2021) 107916, 47pages, arXiv:2101.03573.
  3. Existence of Kirillov-Reshetikhin crystals for near adjoint nodes in exceptional types (joint work with Travis Scrimshaw), Journal of Pure and Applied Algebra 225, issue 5 (2021) 106593, 38pages, arXiv:1903.11681.
  4. Existence of Kirillov-Reshetikhin crystals of type $G_2^{(1)}$ and $D_4^{(3)}$, Journal of Algebra 512 (2018), 47-65, arXiv:1710.11321.
  5. Tensor products of Kirillov-Reshetikhin modules and fusion products, International Mathematics Research Notices 2017 (2017), issue 18, 5667-5709, arXiv:1604.02577.
  6. Graded limits of minimal affinizations over the quantum loop algebra of type G_2 (joint work with Jian-Rong Li), Algebras and Representation Theory 19 (2016), issue 4, 957-973, arXiv:1503.02178.
  7. Defining relations of fusion products and Schur positivity, Toyama Mathmatical Journal 37 (2015), 87-106 (A special issue dedicated to Professor Jun Morita on the occasion of his 60th birthday), arXiv:1504.00109.
  8. Graded limits of minimal affinizations in type D, SIGMA 10 (2014), 047, 20 pages (Contribution to the Special issue on New Directions in Lie Theory), arXiv:1310.5321.
  9. Demazure modules and graded limits of minimal affinizations, Representation Theory 17 (2013), 524-556, arXiv:1210.0175.
  10. Demazure crystals and tensor products of perfect Kirillov-Reshetikhin crystals with various levels, Journal of Algebra 374 (2013), 1-26, arXiv:1108.3139.
  11. Fusion products of Kirillov-Reshetikhin modules and the X=M conjecture, Advances in Mathematics 231 (2012), no. 3-4, 1546-1571, arXiv:1109.2450.
  12. Loewy series of Weyl modules and the Poincaré polynomials of quiver varieties (joint work with Ryosuke Kodera), Publications of RIMS 48 (2012), no. 3, 477-500, arXiv:1103.4207.
  13. Weyl modules, Demazure modules and finite crystals for non-simply laced type, Advances in Mathematics 229 (2012), no. 2, 875-934, arXiv:1012.5480.
  14. Multiloop Lie algebras and the construction of extended affine Lie algebras, Journal of Algebra 323 (2010), no. 8, 2103-2129, arXiv:0807.2019.
  15. On the construction of extended affine Lie algebras using finite order automorphisms, RIMS Kôkyûroku Bessatsu B20 (2010), 21-30. (in Japanese)

Talks

  1. On generalizations of extended T-systems in the category of finite-dimensional modules over a quantum loop algebra, Shinshu Algebra Seminar, Shinshu University, May 2024.
  2. Strong duality data of type A and extended T-systems, Advances in Cluster Algebras 2024, Nagoya University, March 2024 (slides).
  3. Strong duality data of type A and extended T-systems, Tokyo Tech Representation Theory Seminar, Tokyo Institute of Technology, June 2023 (slides).
  4. Generalized quantum affine Schur-Weyl duality and categorical equivalence, 67th Algebra Symposium, RIMS, August 2022 (slides).
  5. Equivalence between module categories over quiver Hecke algebras and Hernandez-Leclerc's subcategories, Quantum Groups and Cluster Algebras, Online, February 2022 (slides).
  6. Equivalence between module categories over quiver Hecke algebras and Hernandez-Leclerc's categories, Conference on Algebraic Representation Theory 2021, Online, November 2021 (slides).
  7. Equivalence via generalized quantum affine Schur-Weyl duality, Algebraic Lie Theory and Representation Theory 2021, Online, June 2021 (slides).
  8. Equivalence via generalized quantum affine Schur-Weyl duality, Minami Osaka algebra Seminar , Online, March 2021 (slides).
  9. Existence of Kirillov-Reshetikhin crystals for the near adjoint nodes in exceptional types, Representation Theory of Algebraic Groups and Quantum Groups -in honor of Professor Ariki's 60th birthday-, RIMS, October 2019 (slides).
  10. Existence of KR crystals in types $G_2^{(1)}$, $D_4^{(3)}$ and $E_6^{(1)}$, Algebraic Lie Theory and Representation Theory 2018, Karuizawa, May 2018 (slides).
  11. Existence of Kirillov-Reshetikhin crystals of type $G_2^{(1)}$ and $D_4^{(3)}$, Infinite Analysis 17 -Algebraic and Combinatorial Aspects in Integrable Systems-, Osaka City University, December 2017.
  12. Noncommutativity between operations of taking tensor product and classical limit of modules over $U_q(L\mathfrak{g})$, MSJ Spring Meeting 2017, Tokyo Metropolitan University, March 2017 (slides).
  13. Finite-dimensional modules over a quantum loop algebra and their classical limits, TUAT Mathematical Seminar 2017, University of Agriculture and Technology, March 2017 (slides).
  14. Noncommutativity between the operations of tensor product and taking a classical limit, Combinatorics of Lie Type, RIMS, October 2016.
  15. Noncommutativity between operations of tensor product and classical limit on modules over a quantum loop algebra, Algebraic Lie Theory and Representation Theory 2016, Nagano, June 2016.
  16. Fusion products of current algebra and Schur positivity, Representation theory, harmonic analysis and differential equation, RIMS, June 2015.
  17. Minimal affinizations and their graded limits, Representation theory and Related Topics, Irako View Hotel, February 2015. (slides)
  18. Jacobi-Trudi formula and quantum loop algebras, Combinatorics Seminar, Tohoku University, December 2014.
  19. Minimal affinizations and their graded limits, Shanghai Workshop on Representation Theory, Tongji University, December 2014.
  20. Minimal affinizations and their graded limits, Conference on Cluster Algebras and Representation Theory , CMC, November 2014. (slides)
  21. Graded limits of finite-dimensional modules over quantum loop algebras, Tsukuba Workshop on Infinite Dimensional Lie Theory and Related Topics -- History and Development --, University of Tsukuba, October 2014. (slides)
  22. Finite-dimensional irreducible representations of a quantum affine algebra and their classical limits, Symposium on Algebra, University of Tokyo, September 2014.
  23. Graded limits of minimal affinizations, Combinatorial representation theory, CRM, April 2014.
  24. An approach to the X=M conjecture using modules over a current algebra, Invited talk in Infinite Analysis session at Mathematical Society of Japan Autumn Meeting 2013, Ehime University, September 2013. (slides)
  25. Finite-dimensional representations over a quantum loop algebra and their classical limits, GT Seminar, Kavli IPMU, May 2013.
  26. Graded limits of minimal affinizations over a quantum loop algebra, Mathematical Society of Japan Spring Meeting 2013, Kyoto University, March 2013. (slides)
  27. An approach to the X=M conjecture using current algebras, Bethe Ansatz, Quantum Groups and Beyond , RIMS, March 2013. (slides)
  28. Graded limits of minimal affinizations, Shanghai workshop on Representation Theory, Osaka University, December 2012.
  29. On minimal affinizations over a quantum affine algebra, Shinshu Algebra Seminar, Shinshu University, November 2012.
  30. On minimal affinizations over a quantum affine algebra of type BC, RIMS Representaion Theory Seminar, RIMS, November 2012.
  31. The X=M conjecture for a quantum affine algebra, MS Seminar, Kavli IPMU, May 2012.
  32. Classical limits of minimal affinizations and generalized Demazure modules, 15th Conference on Representation Theory of Algebraic Groups and Quantum Groups, Nagano, May 2012. (slides)
  33. Loewy series of Weyl modules and the Poincare polynomials of quiver varieties, Lie Theory Seminar, University of California Riverside, February 2012.
  34. Generalized Demazure module and the restricted classical limit of a tensor product of KR modules, Lie Theory Seminar, University of California Riverside, February 2012.
  35. Demazure modules and the X=M conjecture, Shinshu Algebra Seminar, Shinshu University, October 2011.
  36. Demazure modules, Demazure crystals and the X=M conjecture, Topics in Combinatorial Representation Theory, RIMS, October 2011. (slides)
  37. Relations among Weyl modules, Demazure modules and finite crystals, poster session in Infinite Analysis 11, University of Tokyo, July 2011. (poster)
  38. Demazure modules, Demazure crystals and the X=M conjecture, 14th Conference on Representation Theory of Algebraic Groups and Quantum Groups, Kagawa, June 2011.
  39. On the relations among Weyl modules, Demazure modules and the crystal bases of tensor products of fundamental representations, Seminar in Institute of Physics, University of Tokyo, April 2011.
  40. On the relations among Weyl modules, Demazure modules and the crystal bases of tensor products of fundamental representations, RIMS Representation Theory Seminar, RIMS, April 2011.
  41. On the relations among Weyl modules, Demazure modules and the crystal bases of fundamental representations, Osaka Representation Theory Seminar, Osaka, February 2011.
  42. On the relations among Weyl modules, Demazure modules and the crystal bases of fundamental representations, RAQ Seminar, Sophia University, January 2011.
  43. Some relations between the Weyl module and the crystal basis of the tensor product of fundamental representations, Lie Groups and Representation Theory Seminar, University of Tokyo, December 2010.
  44. On the relations among Weyl modules, Demazure modules and finite crystals, Symposium on Representation Theory 2010, Shizuoka, October 2010.
  45. Categorical approach for Weyl modules, after Chari-Fourier-Khandai, MS Seminar, IPMU, August 2009.
  46. On the representation theory of loop algebras and multiloop algebras, Workshop "Algebras, Groups, and Geometry 2009 in Tambara", Tambara Institute of Mathematical Sciences, August 2009.
  47. Construction of extended affine Lie algebras from multiloop Lie algebras, New Viewpoints of Representation Theory and Noncommutative Harmonic Analysis (RIMS Workshop), RIMS, September 2008.
  48. Construction of extended affine Lie algebras from multiloop Lie algebras, Lie Groups and Representation Theory Seminar, University of Tokyo, July 2008.
  49. Construction of extended affine Lie algebras from multiloop Lie algebras, 11th Conference on Representation Theory of Algebraic Groups and Quantum Groups, Okayama, May 2008.
Last updated on May, 16th, 2024.