Toshiaki SHOJI

Graduate School of Mathematics, Nagoya University
Chikusa-ku, Nagoya 464-8602, Japan
TEL: +81 - 52 - 789 - 5605 FAX : +81 - 52 - 789 - 2829 (secretary)
E -mail: shoji AT math.nagoya-u.ac.jp (replace AT by @)
Updated on : January 12, 2005

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To Mathematical Society of Japan, 10th International Research Institute (MSJ-IRI, August 1 - August 10, 2001)
"Representation Theory of Algebraic Groups and Quantum Groups"

To 6th International Conference by Graduate School of mathematics, Nagoya University (June 12 - June 17, 2006)
"Representation Theory of Algebraic Groups and Quantum Groups 06"

To 10th International Conference by Graduate School of Mathematics, Nagoya University (August 2 - August 6, 2010)
"Representation Theory of Algebraic Groups and Quantum Groups '10"

Research Interests

Ordinary represetation theory of finite reductive groups, especially the determinaitn of the character table of such groups, and the geometric aspects related to the theory of character sheaves. The relationship between character sheaves and the theory of Shintani descent.

Representation theory of Ariki-Koike algebras and other cyclotomic Hecke algebras associated to complex reflection groups as a generalization of Hecke algebras of type B_n in conncetion with the representation theory of finite reductive groups.

A generaliztion of the combnatorics related to the symmetric functions such as Schur functions, Hall-Littlewood functions and Green functions of GL_n to the case of other classical groups Sp_{2n}, SO_{2n+1}. I am interested also in generalizing these objects to those related to complex reflection groups G(e,1,n) as a "Weyl group" of non-exsisting classical groups Sp_{en}, SO_{en+1}.

Refresh Corner

GAP manual (Japanese version) : "How to play GAP"

First version (Oct. 2003) PDF, PostScript
Second version (Feb. 2005) PDF, PostScript

Preprints and Notes

Generalized Green functions and unipotent classes for finite reductive groups, II. Preprint. (PDF, PostScript)
A variant of the induction theorem for Springer representations, (revised in July 2006) To appear in J. Algebra. (PDF, PostScript)
Generalized Green functions and unipotent classes for finite reductive groups, I. To appera in Nagoya. Math. J. (PDF, PostScript)
Green functions and Macdonald functions associated to complex reflection groups. Preprint. To appear in the proceedings of the "Conference in Algebras" held in Ateneo de Manila Univesity, 2002. (DVI, PostScript)

Recent Papers

2001

Green functions associated to complex reflection groups. - centering the type D_n. RIMS Kokyuroku "Topics related to combinatorial representation thoery", 2001, 107 - 125. (In Japanese).

Green functions associated to complex reflection groups G(e,1,n). In ``Physics and Combinatorics 2000'', Proceedings of the Nagoya 2000 International Workshop, World Scientific (2001), 281--298. (DVI,   PostScript )

Representations of finite Chevalley groups. Advanced Studies in Pure Math. 32, (2001), 369--378.

Kazhdan-Lusztig basis of Hecke algebras of type B and canonical basis of quantum groups of type A. In the proceedings of the 4th workshop on "Representation theory of Algebraic groups and Quantum groups'', (2001), 41 - 55. (In Japanese, with K. Ohkura)

Green functions associated to complex reflection groups. J. Algebra. 245, (2001), 650 - 694. ( DVI, PostScript )

2002

Green functions associated to complex reflection groups. Sugaku 54, (2002), 69 - 85. (In Japanese)

Green functions associated to complex reflection groups, II. J. Algebra 258, (2002), 563 - 598. (DVI,   PostScript) RT/0105053

On certain bases for Ariki-Koike algebras arising from canonical bases for $U_v(sl_m)$. SUT J. of Math., 38, (2002), 145 - 173. (with K. Ohkura) (DVI,   PostScript)

2003

Macdonald functions associated to complex reflection groups. J. Alg. 260, (2003), 426-448. (DVI,   PostScript) QA/0208061

Generalized Green functions, unipotent classes and graded Hecke algebras. (In Japanese) RIMS Kokyuroku, Combinatorial theoretic representation theory and related topics (2003), 154 - 168.

2004

The work of Susume Ariki---A new interaction between Hecke algebras and quantum groups -- (in Japanese) Sugaku 56 (2004) 194 - 199. (DVI,   PostScript)

Green functions attached to limit symbols. Adv. Studies in Pure Math. 40, "Representation theory of algebraic groups and quantum groups", pp.443 - 467 (2004).

Encyclopedia in Algebra I, The evolution of the group theory, Chapter 3, Visiting the Deligne-Lusztig characters -- Representation theory of finite Chevalley groups --, pp.185 -- 326, (with Hotta, Watanabe, and Mimachi), (in Japanese). Asakura, Tokyo (2004)

Lusztig's conjecture for special linear groups. (in Japanese) RIMS Kokyuroku, "Aspects of the combinatorial representation theory". (2004), 80 -- 89. (PDF,   PostScript)

Subfield symmetric spaces for finite special linear grouups. Representation theory, an Electronic J. of AMS, 8 (2004) 487 -- 521 (with K. Sorlin). (PDF,   PostScript)

2005

Modified Ariki-Koike algebras and cyclotomic $q$-Schur algebras, Math. Z. 249, (2005) 829--867 (with N.Sawada). (DVI,   PostScript)

On Green functions assocaited to complex reflection groups. Sugaku Expositions 18, (2005) 123--141. (DVI,   PostScript)

Flash beams in representation theroy -- seven stories centering Hecke algebras -- (in Japanese) Suuri-Kagaku, December 2005, 15 -- 21.

2006

Symmetric space assocaited to finite special linear groups, Proceedings of the conference on groups and Lie algebras, Sophia Univ. Lecture series on Mathematics No. 46, (2006), 119 -- 137.

Schur-Weyl reciprocity between quantum groups and Hecke algerbas of type $G(p,p,n)$. (with J. Hu) J. of Algebra, 298 (2006), 215 -- 237.

Lusztig's conjecture for finite special linear groups. Representation Theory, an Electronic J. of AMS, 10, (2006) 164--222. (PDF,   PostScript)

On the computation of irreducible characters of finite reductive \ groups. RIMS Kokyuroku: "The world of combinatorial representation theory" (2006) 140 -- 153.

Publications