# Jian Yi Shi          ÖÐÎÄ°æ

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, 200241, P. R. China Office room 333, Mathematical Building +86 021 62451486 (H); +86 021 54345064 (O) jyshi@math.ecnu.edu.cn, jyshi11@yahoo.com

### Research Interests

Algebraic groups and representation theory. Combinatorics

Publications and 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. first edition; 2009, second edition.

#### Papers

 Reduced expressions for the elements in a Bruhat interval, To appear in Discrete Math.
 The boundedness of a weighted Coxeter group with non-3-edge-labeling graph, To appear in Journal of Algebra and Its Applications, (2019)
 Some left cells in the affine Weyl group E_6~, Comm. in Algebra, 46(5) (2018), 2033--2053
 Kazhdan-Lusztig cells in some weighted Coxeter groups, Science China Math., 61(2) (2018), 325--352
 The relation \leq_{LR} on some elements of the affine Weyl group C_n~, Journal of Algebra, 479 (2017), 78--101
 The boundness of the weighted Coxeter group with complete graph, with G. Yang, Proc. AMS,144(11) (2016), 4573--4581
 The cells in the weighted Coxeter group (C_n,l_m), Journal of Algebra, 443C (2015), 13--32
 The weighted universal Coxeter group and some related conjectures of Lusztig, with G. Yang, Journal of Algebra, 441C (2015), 678-694
 Left-connectedness of left cells in the Weyl group of type E6, with Q. Q. Mi, Huadong Shifan Daxue Xuebao(Natural Sicience), no.1(2013), 76--90
 The cells of the affine Weyl group C_n in a certain quasi-split case, II, Journal of Algebra, 404C(2014), 31--59
 The reduced expressions in a Coxeter system with a strictly complete Coxeter graph, Adv. in Math., 272 (26)(2015), 579--597
 Left cells of the weighted Coxeter group (B_n,l), with Q. Q. Mi, Comm. Algebra, 43 (4)( 2015),1487--1508
 Some cells in the weighted Coxeter group (C_n,l_{2n+1}), with Q. Huang, Journal of Algebra, 395(2013),63--81
 The left cells with a-values 5,6 in the affine Weyl group E_8, with Q. Huang, Australasian Journal of Combinatorics, 56(2013), 153--182 (shorttext)
 The left cells with a-values 5,6 in the affine Weyl group E_8, with Q. Huang, preprint (fulltext)
 The cells of the affine Weyl group C_n in a certain quasi-split case, Journal of Algebra, 422C (2015), 697--729
 The Laurent polynomials M^s_{y,w} in the Hecke algebra with unequal parameters,  Journal of Algebra,357(1)(2012),1--19
 Left cells in the affine Weyl group E6, with X. G. Zhang,  preprint
 Left cell graphs in the affine Weyl group E6, with X. G. Zhang,  preprint
 A new algorithm for finding an l.c.r. set in certain two-sided cells,  Pacific Journal of Mathematics 256(1)(2012),235--252
 The second lowest two-sided cell in an affine Weyl group,  Journal of Algebra 357(1)(2011), 161--179
 Reflection ordering on the groups G(m,m,n),   Journal of Pure and Applied Algebra, 215 (5) (2011), 741--752
 Reflection subgroups and sub-root systems of the imprimitive complex reflection groups,   with L. Wang, Science in China, Series A, Mathematics, 53 (6) (2010), 1595-1602
 A counter-example to a conjecture of Lusztig,   Journal of Algebra, 323 (2010), 2591--2598
 Some primitive linear groups of prime degree, with M. C. Kang, J. P. Zhang, Y. Yu, Stephen T. Yau,  Journal of the Mathematical Society of Japan, 61 (4) (2009), 1013-1070
 Automorphism Groups of the Imprimitive Complex Reflection Groups G(m,p,n), with L. Wang, Journal of Australian Math. Society, 86 (2009), 123--138
 Reflection ordering on the groups G(m,p,n),  Journal of Algebra, 319 (11) (2008), 4646--4661
 ,  Journal of Algebra, 319 (6) (2008), 2410--2433.
 , with X. G. Zhang, Comm. in Algebra. 36 (9)(2008), 3317--3346 ¡¡ Joint relations on elements of the symmetric group, Journal of Algebra, 319 (8) (2008), 3197--3221 Formula for the reflection length of elements in the group G(m,p,n), Journal of Algebra. 316 (1) (2007), 284--296 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}, Advances in Mathematics, 177 (2) (2003), 181-207 Coxeter elements and Kazhdan-Lusztig cell,  Journal of 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,  Advances in Mathematics, 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 posets,  J. 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,  Journal of Algebra, 202 (1998), 745-776. Left cells in the affine Weyl group of type F_4,   Journal of 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,  Journal of 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,    Journal of 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.