Generalized quotients in Coxeter groups
نویسندگان
چکیده
منابع مشابه
Essays on Coxeter groups Coxeter elements in finite Coxeter groups
A finite Coxeter group possesses a distinguished conjugacy class of Coxeter elements. The literature about these is very large, but it seems to me that there is still room for a better motivated account than what exists. The standard references on thismaterial are [Bourbaki:1968] and [Humphreys:1990], butmy treatment follows [Steinberg:1959] and [Steinberg:1985], from which the clever parts of ...
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We define and study generalized nil-Coxeter algebras associated to Coxeter groups. Motivated by a question of Coxeter (1957), we construct the first examples of such finite-dimensional algebras that are not the ‘usual’ nil-Coxeter algebras: a novel 2-parameter type A family that we call NCA(n, d). We explore several combinatorial properties of NCA(n, d), including its Coxeter word basis, length...
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The principal objects studied in this note are Coxeter groups W that are neither finite nor affine. A well known result of de la Harpe asserts that such groups have exponential growth. We consider quotients of W by its parabolic subgroups and by a certain class of reflection subgroups. We show that these quotients have exponential growth as well. To achieve this, we use a theorem of Dyer to con...
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We generalize some identities and q-identities previously known for the symmetric group to Coxeter groups of type B and D. The extended results include theorems of Foata and Schützenberger, Gessel, and Roselle on various distributions of inversion number, major index, and descent number. In order to show our results we provide caracterizations of the systems of minimal coset representatives of ...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1988
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1988-0946427-x