无限Coxeter群、无限Weyl群、无限反射群p-adic Chevalley、无限Chevalley群等领域的简介(其中的无限群指元素个数为无限的群,包含拓扑群、李群、典型群、代数群、算术群等),其中Coxeter群既是代数学的领域也属于我们组合数学的领域:

有限Coxeter群(其中特别说Richard Brauer理查德·布饶尔大师在哈佛大学指导并到海南琼州大学的导师去合作几年的威斯康星大学任教的Louis Solomon博士工作):

在美国数学评论见这领域第一篇论文海南琼州大学的导师柳柏濂教授去美国合作几年诞生教育部审定通过的中国“第一本”数学研究生用书的美国威斯康星大学的教授Louis Solomon独撰的这篇论文A decomposition of the group algebra of a finite Coxeter group. J. Algebra 9 (1968), 220--239.

È. B. Vinberg, Geometric representations of Coxeter groups. (Russian) Uspehi Mat. Nauk 25 (1970), no. 2(152), 267--268.

C. T. BensonL. C. Grove, Generators and relations for Coxeter groups. Proc. Amer. Math. Soc. 24 (1970), 545--547.

I. G. Macdonald, The Poincaré series of a Coxeter group. Math. Ann. 199 (1972), 161--174.

I. G. Macdonald, On the degrees of the irreducible representations of finite Coxeter groups. J. London Math. Soc. (2) 6 (1973), 298--300.

A. van den Hombergh, About the automorphisms of the Bruhat-ordering in a Coxeter group. Nederl. Akad. Wetensch. Proc. Ser. A 77. Indag. Math. 36 (1974), 125--131.

George Maxwell独撰的The crystallography of Coxeter groups. J. Algebra 35 (1975), 159--177.

C. M. CampbellE. F. Robertson, Applications of the Todd-Coxeter algorithm to generalised Fibonacci groups. Proc. Roy. Soc. Edinburgh Sect. A 73 (1975), 163--166.

上面海南琼州大学的导师去合作几年的威斯康星大学的教授Louis Solomon独撰在组合数学杂志发表的相关论文The Burnside algebra of a finite group. J. Combinatorial Theory 2 (1967), 603--615.

上面海南琼州大学的导师去合作几年的威斯康星大学的教授Louis Solomon独撰在组合数学杂志发表的相关论文On the Poincaré-Birkhoff-Witt theorem. J. Combinatorial Theory 4 (1968), 363--375.

Rober Kilmoyer上面海南琼州大学的导师去合作几年的威斯康星大学的教授Louis Solomon合作在组合数学杂志发表的相关论文On the theorem of Feit-Higman. J. Combinatorial Theory Ser. A 15 (1973), 310--322.

上面海南琼州大学的导师去合作几年的威斯康星大学的教授Louis Solomon独撰在组合数学杂志发表的相关论文Partition identities and invariants of finite groups. J. Combinatorial Theory Ser. A 23 (1977), no. 2, 148--175.

上面海南琼州大学的导师去合作几年的威斯康星大学的教授Louis Solomon独撰的A Mackey formula in the group ring of a Coxeter group. J. Algebra 41 (1976), no. 2, 255--264.(他作为美国数学及其应用联合会(COMAP)的主席)

在我们组合数学杂志发表的Gareth A. Jones独撰的Just-edge-transitive maps and Coxeter groups. Ars Combin. 16 (1983), B, 139--150.(英国组合数学委员会主席Peter J. Cameron同于1971年在牛津大学博士毕业的师兄弟);

Peter Orlik上面海南琼州大学的导师去合作几年的威斯康星大学的教授Louis Solomon合作在组合数学杂志发表的相关论文Arrangements in unitary and orthogonal geometry over finite fields. J. Combin. Theory Ser. A 38 (1985), no. 2, 217--229.

Peter Orlik上面海南琼州大学的导师去合作几年的威斯康星大学的教授Louis Solomon合作发表的组合数学论文Combinatorics组合数学 and topology of complements of hyperplanes. Invent. Math. 56 (1980), no. 2, 167—189

上面海南琼州大学的导师去合作几年的威斯康星大学的教授Louis Solomon发表的组合数学论文Partially ordered sets with colors. Relations between combinatorics and other parts of mathematics (Proc. Sympos. Pure Math., Ohio State Univ., Columbus, Ohio, 1978), pp. 309--329,

无限Coxeter群:

George Maxwell独撰的On the crystallography of infinite Coxeter groups. Math. Proc. Cambridge Philos. Soc. 82 (1977), no. 1, 13--24.

Kenneth Ira AppelPaul Eugene Schupp合写的“Artin groups and infinite Coxeter groups”,Invent. Math. 72 (1983), no.2,201--220.

等等。

 

无穷反射群:

开创上面Coxeter”领域的H. S. MCoxeter,的论文The product of the generators of a finite group generated by reflections. Duke Math. J. 18 (1951), 765--782.

开创下面Chevalley”领域的Claude.Chevalley的论文Invariants of finite groups generated by reflections. Amer. J. Math. 77 (1955), 778--782.

上面海南琼州大学的导师去合作几年的威斯康星大学的教授Louis Solomon的论文Invariants of finite reflection groups. Nagoya Math. J. 22 (1963), 57--64.

上面海南琼州大学的导师去合作几年的威斯康星大学的教授Louis Solomon的论文Invariants of Euclidean reflection groups. Trans. Amer. Math. Soc. 113 (1964), 274--286.

等等

 

Chevalley群、p-adic Chevalley群:

Rimhak Ree独撰的的论文On some simple groups defined by C. Chevalley. Trans. Amer. Math. Soc. 84 (1957), 392--400.Rimhak Ree的导师Stephen Arthur Jennings上面海南琼州大学的导师去合作几年的威斯康星大学的教授Louis Solomon的师兄

Abe, Eiichi. On the groups of C. Chevalley. J. Math. Soc. Japan 11 (1959), 15--41.

Iwahori, Nagayoshi. On the structure of a Hecke ring of a Chevalley group over a finite field. J. Fac. Sci. Univ. Tokyo Sect. I 10 (1964), 215--236 (1964).

Iwahori, N.; Matsumoto, H. On some Bruhat decomposition and the structure of the Hecke rings of p-adic Chevalley groups. Inst. Hautes Études Sci. Publ. Math. No. 25, (1965), 5--48.

Robert Steinberg独撰的277页书籍《Lectures on Chevalley groups. Notes prepared by John Faulkner and Robert Wilson. Yale University, New Haven, CT, 1968. 277 pp.Robert Steinberg上面海南琼州大学的导师去合作几年的威斯康星大学的教授Louis Solomon的师兄)

日本组合数学大师Hikoe Enomoto的论文The conjugacy classes of Chevalley groups of type (G2) over finite fields of characteristic 2 or 3. J. Fac. Sci. Univ. Tokyo Sect. I 16 (1969), 497--512 (1970).

Shalika, J. A. On the space of cusp forms of a P-adic Chevalley group. Ann. of Math. (2) 92 (1970), 262--278.

无限Chevalley群(可见这方向进展缓慢):

Humphreys, J. E. On the automorphisms of infinite Chevalley groups. Canadian J. Math. 21 (1969), 908--911.

Novodvorskiĭ, M. E. Certain fixed vectors in infinite-dimensional representations of Chevalley groups. (Russian) Funkcional. Anal. i Priložen. 5 (1971), no. 1, 87--88.

Sawada, Hideki. Some infinite-dimensional indecomposable modules of Chevalley groups. Arch. Math. (Basel) 36 (1981), no. 5, 414--422.