Jian Yi Shi          ÖÐÎİæ

I am a Professor in the Department of Mathematics at the East China Normal University.

Jian Yi Shi, Department of Mathematics, East China Normal University, Shanghai, 200062, P. R. China
Office 204,
+86 021 62451486 (H); +86 021 54345060 (O)
+86 021 62232475(Fax)
jyshi@math.ecnu.edu.cn

Research Interests

Algebraic groups and representation theory. Combinatorics


Publications

Preprints

Book

* The Kazhdan-Lusztig cells in certain affine Weyl groups, Lecture Notes in Math., vol. 1179, Springer-Verlag, 1986.
* Representation theory of finite groups, with Cao Xihua, Advanced Educational Publication House, 1992.

Papers

* Left-connectedness of some left cells in certain Coxeter groups of simply-laced type,  To appear in Journal of Algebra.
* Left cells with a-value 4 in the affine Weyl groups E_i (i=6,7,8),  To appear in Comm. in Algebra.
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* Automorphism Groups of the Imprimitive Complex Reflection Groups G(m,p,n),  To appear in Journal of Australian Math. Society.
* Joint relations on elements of the symmetric group,  To appear in J. Algebra.
* Formula for the reflection length of elements in the group G(m,p,n),  To appear in J. Algebra.
* Presentations for finite complex reflection groups,  Proceedings of the Conference on Complex geometry, Algebra, and Combinatorics, AMS/IP Studies in Advanced Mathematics, 39(2007), 263--275. 
* Left cells containing a fully commutative element,  J. Comb. Theory (Series A) 113(2006), 556--565.
* Lower boundary hyperplanes of the canonical left cells in the affine Weyl group W_a(A_{n-1}),  Pacific J. Math. 226(2)(2006), 389--398.
* Congruence classes of presentations for the complex reflection groups G(m,1,n) and G(m,m,n),   Indagationes Mathematicae N. S. 16(2)(2005), 267--288.
* Fully commutative elements and Kazhdan--Lusztig cells in the finite and affine Coxeter groups, II,  J. Proc. Amer. Math. Soc.  133 (2005), 2525--2531.
* Simple root systems and presentations for certain complex reflection groups,  Comm. in Algebra, 33 (2005), 1765--1783.
* Congruence classes of presentations for the complex reflection groups G(m,p,n),  J. Algebra, 284 (1) (2005), 392--414.
* Fully commutative elements in the Weyl and affine Weyl groups,  J. Algebra, 284 (1)(2005), 13--36.
* The order of a root of x^p-x-1 over F_p, with Zheng-hua Wang. Huadong Shifan Daxue Xuebao. (2004), 1--4
* Fully commutative elements and Kazhdan-Lusztig cells in the finite and affine Coxeter groups, Proc. AMS. 131(2003),3371-3378
* Explicit formulae for the Brenti's polynomials  G_{a_1,...,a_r}, Adv. in Math. 177(2)(2003), 181-207
* Coxeter elements and Kazhdan-Lusztig cells,  J. Algebra 250 (2002), 229-251.
* Certain imprimitive reflection groups and their generic version,  Transactions Amer. Math. Soc. 354(5) (2002), 2115-2129.
* Conjugacy relations on Coxeter elements,  Adv. in Math., 161 (2001), 1-19.
* On regularity of finite reflection groups, with B. R. Howlett. manuscripta mathematica, 102 (2000), 325-333.
* On two presentations of the affine Weyl groups of classical types, J. Algebra, 221 (1999), 360-383.
* Sign types associated to posetsJ. Comb. Theory (Ser. A), 88 (1999), 36-53.
* Left cells of the Weyl group of type E_7, with Chen Yu. Comm. in Algebra, 26 (1998), 3837-3852.
* Left cells in the affine Weyl group of type C_4, J. Algebra, 202 (1998), 745-776.
* Left cells in the affine Weyl group of type F_4J. Algebra., 200 (1998), 173-206.
* The number of  $\oplus$-sign types, Quarterly J. Math., Oxford, 48 (1997), 93-105.
* The enumeration of Coxeter elements, J. Comb. Algebra, 6 (1997), 161-171.
* The partial order on two-sided cells of certain affine Weyl groups, J. Algebra, 179 (1996), 607-621.
* Left cells in certain Coxeter groups, in book " Group Theory in China ", Z. Wan and S. Shi eds., Kluwer Publishers, New York,   1996.
* The verification of a conjecture on left cells of certain affine Coxeter groups, Hiroshima J. Math., 24 (1994), 627-646.
* Some results relating two presentations of certain affine Weyl groups, J. Algebra, 163 (1994), 235-257.
* Left cells in the affine Weyl group W_a(D_4), Osaka J. Math., 31 (1994), 27-50. 
* Left cells in the affine Weyl groups, Tohoku J. Math., 46 (1994), 105-124.
* Some numeric results on root systems, Pacific J. Math., 160 (1993), 155-164.
* Skew tableaux, lattice paths and bounded partitions, J. Comb. Theory (Ser. A), 63 (1993), 79-89.
* The generalized Robinsin-Schensted algorithm in the affine Weyl group of type A_{n-1},, J. Algebra, 139 (1991), 364-394.
* The joint relations and the set $D_1$ in certain crystallographic groups, Adv. in Math., 81 (1990), 66-89.
* A result on the Bruhat order of a Coxeter group, J. Algebra, 128 (1990), 510-516.
* A survey on the cell theory of affine Weyl groups, Adv. Sci. China (Mathematics), 3 (1989), 79-98.
* Some recent developments on the cells of affine Weyl groups, in book "Classical groups and related topics ", Cont. Math. Amer. Math. Soc., 82 (1989), 159-169.
* A two-sided cell in an affine Weyl group, II,  J. London Math. Soc., 37 (1988), 253-264.
* A two-sided cell in an affine Weyl group,   J. London Math. Soc., 36 (1987), 407-420.
* Sign types corresponding to an affine Weyl group,  J. London Math. Soc., 35 (1987), 56-74.
* Alcoves corresponding to an affine Weyl group,  J. London Math. Soc., 35 (1988), 42-55.
* The results on the cells of the affine Weyl groups of type A,  J. Northeastern Math., 2 (1986), 196-204.

Some interesting links