无限Coxeter群、无限Weyl群、无限反射群、p-adic Chevalley群、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是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. Benson,L. 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. Campbell,E. 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和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和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和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 Appel和Paul 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群”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群”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是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是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.