CURRICULUM VITAE Tatsuro Ito

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1 CURRICULUM VITAE Tatsuro Ito Personal Details Date of Birth: 25 October 1948 Nationality: Japanese Office: School of Mathematical Sciences, Anhui University, 111 Jiulong Road, Hefei , China tel: Education 1972: B.Sc. in Mathematics, University of Tokyo 1974: M.Sc. in Mathematics, University of Tokyo : British Council Scholar, Royal Holloway College, University of London 1982: D.Sc. in Mathematics, University of Tokyo Appointments 2014 : Chair Professor, Anhui University : Professor, Kanazawa University : Visiting Professor, Kyushu University : Professor, Osaka Kyoiku University : Visiting Associate Professor, Ohio State University : Associate Professor, Joetsu Kyoiku University : Visiting Assistant Professor, Ohio State University : Assistant Professor, Tsukuba University : Assistant Professor, Tokyo Kyoiku University 1

2 Administrative Activities (selected) : Chairman, Dept of Computational Science, Kanazawa Univ : Chairman, Dept of Computational Science, Kanazawa Univ : Chairman, Dept of Computational Science, Kanazawa Univ JSPS Grant (Tatsuro Ito) : Grant-in-Aid for challenging Exploratory Research Y=3,510,000=1,170,000+1,040,000+1,300,000 A study on the q-analogue of symmetric spaces in the framework of association schemes : Grant-in-Aid for Scientific Research (B) Y=16,610,000=5,300,000+3,770,000+3,770,000+3,770,000 Representations of Terwilliger algebras and their applications : Grant-in-Aid for Scientific Research (B) Y=10,000,000=2,400,000+2,400,000+2,300,000+2,900,000 Representations of Terwilliger algebras and their applications 1996: Grant-in-Aid for Specially Promoted Research Y=500,000 T-module structures of association schemes attached to spin models 1991: Grant-in-Aid for Scientific Research (C) Y=1,500,000 Algebraic Combinatorics and Related Areas 1988: Grant-in-Aid for Scientific Research (C) Y=800,000 Algebraic Combinatorics 2

3 Invited Lectures of Recent Years (Tatsuro Ito) (selected) 1. The classification of TD-pairs, Hour talk, RIMS Symposium Finite Groups and their Representations, Vertex Operator Algebras, Algebraic Combinatorics, RIMS, March The classification of TD-pairs of Type II, Hour talk, Workshop on Algebraic combinatorics, Hebei Normal University, November, Leonard pairs and the q-racah polynomials, 6 Lectures for the 3rd Rogla PhD Summer School, Rogla, Slovenia, June Leonard piars and Askey-Wilson polynomials, 8 Lectures for Intensive Course, Shimane University, December The Pfaff-Saalschütz summation formula revisited, Hour talk, Workshop on Algebraic Combinatorics, Shanghai Jiao Tong University, August Finite dimensional irreducible representations of certain subalgebras of the quantum affine algebra U q (ŝl 2), Hour talk, Workshop on Algebraic Combinatorics, Shanghai Jiao Tong University, September The Drinfel d polynomial for a tridiagonal pair, Hour talk, Workshop on Algebraic Combinatorics, Hebei Normal University, November Tridiagonal pairs and the q-onsager algebra, Hour talk, The 55th Symposium on Algebra, Hokkaido University, August Towards the classification of P- and Q- polynomial association schemes, Hour talk, JAIST Workshop on METRIC GRAPH THEORY, Kanazawa Culture Hall, Kanazawa, November Irreducible representations of Terwilliger algebras for P- and Q-polynomial association schemes, Hour talk, The 25th Conference on Algebraic Combinatorics, Hokkaido University, June The q-onsager algebra and its finite dimensional irreducible representations, Hour talk, The second Internatinal Congress in Algebra and Combinatorics, Beihang University, Beijing, China, July

4 Publications (Tatsuro Ito) 1. E.Bannai and T.Ito, On finite Moore graphs, J. Fac. Sci., University of Tokyo, Sec.1A, 20 (1973), T.Ito, Primitive rank 5 permutation groups with two doubly transitive constituents of different sizes, J. Fac. Sci., University of Tokyo, Sec.1A, 21 (1974), E.Bannai and T.Ito, On the spectra of certain distance-regular graphs, J. Comb. Theory (B), 27 (1979), E.Bannai and T.Ito, On the spectra of certain distance-regular graphs II, Quart. J. Math. Oxford (2), 32 (1981), T.Ito and M.Kiyota, Sharp permutation groups, J. Math. Soc. Japan, 33 (1981), E.Bannai and T.Ito, Regular graphs with excess one, Discrete Math., 37 (1981), N.Biggs and T.Ito, Graphs with even girth and small excess, Math. Proc. Camb. Phil. Soc., 88 (1980), T.Ito, On a graph of O Keefe and Wong, J. Graph Theory, 5 (1981), T.Ito, Bipartite distance-regular graphs of valency three, Linear Algebra Appl., 46 (1982), E.Bannai and T.Ito, Algebraic Combinatorics I: association schemes, Benjamin/Cummings Lecture Note Series, Menlo Park, E.Bannai and T.Ito, Current researches on algebraic combinatorics, Graphs and Combinatorics, 2 (1986), E.Bannai and T.Ito, On distance-regular graphs with fixed valency, Graphs and Combinatorics, 3 (1987), E.Bannai and T.Ito, On distance-regular graphs with fixed valency II, Graphs and Combinatorics, 4 (1988),

5 14. E.Bannai and T.Ito, 0n distance-regular graphs with fixed valency III, J. of Algebra, 107 (1987), E.Bannai and T.Ito, On distance-regular graphs with fixed valency IV, Europ. J. Combinatorics, 10 (1989), T.Ikuta, T.Ito and A.Munemasa, On pseudo-automorphisms and fusions of an association scheme, Europ. J. Combinatorics, 12 (1991), T.Ito, A.Munemasa and M.Yamada, Amorphous association schemes over the Galois rings of characteristic 4, Europ. J. Combinatorics, 12 (1991), S.Hobart and T.Ito, The structure of nonthin irreducible T-modules of endpoint 1: ladder bases and classical parameters, J. Algebraic Combinatorics, 7 (1998), H.Ishibashi, T.Ito and M.Yamada, Terwilliger Algebras of Cyclotomic Schemes and Jacobi Sums, Europ. J. Combinatorics, 20 (1999), T.Ito, K.Tanabe and P.Terwilliger, Some algebra related to P- and Q-polynomial association schemes, Codes and association schemes (Piscataway, NJ, 1999), , DIMACS Ser. Discrete Math. Theoret. Comput. Sci., 56, Amer. Math. Soc., Providence, RI, T.Ito, Designs in a coset geometry: Delsarte theory revisited, European J. Combin. 25 (2004), T.Ito and P.Terwilliger, The shape of a tridiagonal pair, J. Pure Appl. Algebra 188 (2004), Tatsuro Ito, Paul Terwilliger and Chih-wen Weng, The quantum algebra U q (sl 2 ) and its equitable presentation, J. Algebra 298 (2006), T.Ito and P.Terwilliger, Tridiagonal pairs and the quantum affine algebra U q (ŝl 2), Ramanujan J. 13 (2007), T.Ito and P.Terwilliger, The q-tetrahedron algebra and its finite dimensional irreducible modules, Comm. Algebra 35 (2007),

6 26. T.Ito and P.Terwilliger, Two non-nilpotent linear transformations that satisfy the cubic q-serre relations, J. Algebra Appl. 6 (2007), T.Ito and P.Terwilliger, q-inverting pairs of linear transformations and the q-tetrahedron algebra, Linear Algebra Appl. 426 (2007), T.Ito and P.Terwilliger, Tridiagonal pairs of Krawtchouk type, Linear Algebra Appl. 427 (2007), T.Ito and P.Terwilliger, Finite-dimensional irreducible modules for the three-point sl 2 loop algebra, Comm. Algebra 36 (2008), T.Ito and P.Terwilliger, Distance-regular graphs and the q-tetrahedron algebra, Europ. J. of Combinatorics 30 (2009), no. 3, T.Ito and P.Terwilliger, Distance-regular graphs of q-racah type and the q-tetrahedron algebra, Michigan Mathematical Journal 58 (2009), T.Ito and P.Terwilliger, The Drinfel d polynomial of a tridiagonal pair, J. of Combinatorics, Information and System Sciences 34 (2009), T.Ito and P.Terwilliger, Tridiagonal pairs of q-racah type, J. Algebra 322 (2009), T.Ito and P.Terwilliger, The augmented tridiagonal algebra, Kyushu J. Math. 64 (2010), T.Ito and P.Terwilliger, How to sharpen a tridiagonal pair, J. Algebra Appl. 9 (2010), T.Ito and P.Terwilliger, An algebra generated by two sets of mutually orthogonal idempotents, J. Algebra Appl. 9 (2010), T.Ito and P.Terwilliger, Double affine Hecke algebras of rank 1 and the Z3-symmetric Askey-Wilson relations, SIGMA 6 (2010), 065, 9 pages. 38. T.Ito and P.Terwilliger, Mock tridiagonal systems, Linear Algebra Appl. 435 (2011),

7 39. T.Ito, K.Nomura and P.Terwilliger, A classification of sharp tridaiagonal pairs, Linear Algebra Appl. 435 (2011), T.Ito, TD-pairs and the q-onsager algebra, Sugaku 65 (2013), (in Japanese). 41. Tatsuro Ito, Hjalmar Rosengren, and Paul Terwilliger, Evaluation modules for the q-tetrahedron algebra, Linear Algebra Appl. 451 (2014) Tatsuro Ito and Jugo Sato, TD-pairs of type II with shape 1,2,..., 2,1, Linear Algebra Appl. 461 (2014)

How to sharpen a tridiagonal pair

How to sharpen a tridiagonal pair Tatsuro Ito and Paul Terwilliger arxiv:0807.3990v1 [math.ra] 25 Jul 2008 Abstract Let F denote a field and let V denote a vector space over F with finite positive dimension.