Japanese English

Institute of Engineering, Tokyo University of Agriculture and Technology

2-24-16 Naka-cho, Koganei-shi, Tokyo 184-8588, JAPAN

naoik_at_cc.tuat.ac.jp

- Papers and Preprints
- Talks
- Curriculum Vitae

- Existence of Kirillov-Reshetikhin crystals of type $G_2^{(1)}$ and $D_4^{(3)}$, to appear in Journal of Algebra,
arXiv:1710.11321.
- Tensor products of Kirillov-Reshetikhin modules and fusion products,
International Mathematics Research Notices 2017 (2017),
issue 18, 5667-5709, arXiv:1604.02577.

- 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.

- 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.

- 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.

- Demazure modules and graded limits of minimal affinizations, Representation Theory 17 (2013), 524-556, arXiv:1210.0175.

- Demazure crystals and tensor products of perfect Kirillov-Reshetikhin crystals with various levels,
Journal of Algebra 374 (2013), 1-26,
arXiv:1108.3139.

- Fusion products of Kirillov-Reshetikhin modules and the X=M conjecture, Advances in Mathematics 231 (2012), no. 3-4, 1546-1571,
arXiv:1109.2450.

- 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.

- Weyl modules, Demazure modules and finite crystals for non-simply laced type, Advances in Mathematics 229 (2012), no. 2, 875-934, arXiv:1012.5480.

- Multiloop Lie algebras and the construction of extended affine Lie algebras, Journal of Algebra 323 (2010), no. 8, 2103-2129, arXiv:0807.2019.
- On the construction of extended affine Lie algebras using finite order automorphisms, RIMS Kôkyûroku Bessatsu B20 (2010), 21-30. (in Japanese)

- Existence of KR crystals in types $G_2^{(1)}$, $D_4^{(3)}$ and $E_6^{(1)}$, Algebraic Representation Theory and Representation Theory 2018, Karuizawa, May 2018.
- 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.
- 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).
- Finite-dimensional modules over a quantum loop algebra and their classical limits, TUAT Mathematical Seminar 2017, University of Agriculture and Technology, March 2017 (slides).
- Noncommutativity between the operations of tensor product and taking a classical limit, Combinatorics of Lie Type, RIMS, October 2016.
- 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.
- Fusion products of current algebra and Schur positivity, Representation theory, harmonic analysis and differential equation, RIMS, June 2015.
- Minimal affinizations and their graded limits, Representation theory and Related Topics, Irako View Hotel, February 2015. (slides)
- Jacobi-Trudi formula and quantum loop algebras, Combinatorics Seminar, Tohoku University, December 2014.
- Minimal affinizations and their graded limits, Shanghai Workshop on Representation Theory, Tongji University, December 2014.
- Minimal affinizations and their graded limits, Conference on Cluster Algebras and Representation Theory , CMC, November 2014. (slides)
- 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)
- Finite-dimensional irreducible representations of a quantum affine algebra and their classical limits, Symposium on Algebra, University of Tokyo, September 2014.
- Graded limits of minimal affinizations, Combinatorial representation theory, CRM, April 2014.
- 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)
- Finite-dimensional representations over a quantum loop algebra and their classical limits, GT Seminar, Kavli IPMU, May 2013.
- Graded limits of minimal affinizations over a quantum loop algebra, Mathematical Society of Japan Spring Meeting 2013, Kyoto University, March 2013. (slides)
- An approach to the X=M conjecture using current algebras, Bethe Ansatz, Quantum Groups and Beyond , RIMS, March 2013. (slides)
- Graded limits of minimal affinizations, Shanghai workshop on Representation Theory, Osaka University, December 2012.
- On minimal affinizations over a quantum affine algebra, Shinshu Algebra Seminar, Shinshu University, November 2012.
- On minimal affinizations over a quantum affine algebra of type BC, RIMS Representaion Theory Seminar, RIMS, November 2012.
- The X=M conjecture for a quantum affine algebra, MS Seminar, Kavli IPMU, May 2012.
- Classical limits of minimal affinizations and generalized Demazure modules, 15th Conference on Representation Theory of Algebraic Groups and Quantum Groups, Nagano, May 2012. (slides)
- Loewy series of Weyl modules and the Poincare polynomials of quiver varieties, Lie Theory Seminar, University of California Riverside, February 2012.
- Generalized Demazure module and the restricted classical limit of a tensor product of KR modules, Lie Theory Seminar, University of California Riverside, February 2012.
- Demazure modules and the X=M conjecture, Shinshu Algebra Seminar, Shinshu University, October 2011.
- Demazure modules, Demazure crystals and the X=M conjecture, Topics in Combinatorial Representation Theory, RIMS, October 2011. (slides)
- Relations among Weyl modules, Demazure modules and finite crystals, poster session in Infinite Analysis 11, University of Tokyo, July 2011. (poster)
- Demazure modules, Demazure crystals and the X=M conjecture, 14th Conference on Representation Theory of Algebraic Groups and Quantum Groups, Kagawa, June 2011.
- 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.
- 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.
- On the relations among Weyl modules, Demazure modules and the crystal bases of fundamental representations, Osaka Representation Theory Seminar, Osaka, February 2011.
- On the relations among Weyl modules, Demazure modules and the crystal bases of fundamental representations, RAQ Seminar, Sophia University, January 2011.
- 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.
- On the relations among Weyl modules, Demazure modules and finite crystals, Symposium on Representation Theory 2010, Shizuoka, October 2010.
- Categorical approach for Weyl modules, after Chari-Fourier-Khandai, MS Seminar, IPMU, August 2009.
- 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.
- Construction of extended affine Lie algebras from multiloop Lie algebras, New Viewpoints of Representation Theory and Noncommutative Harmonic Analysis (RIMS Workshop), RIMS, September 2008.
- Construction of extended affine Lie algebras from multiloop Lie algebras, Lie Groups and Representation Theory Seminar, University of Tokyo, July 2008.
- Construction of extended affine Lie algebras from multiloop Lie algebras, 11th Conference on Representation Theory of Algebraic Groups and Quantum Groups, Okayama, May 2008.