اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدCombinatorial representations of Coxeter groups over a field of two elements
456
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Let $W$ denote a simply-laced Coxeter group with $n$ generators. We construct an $n$-dimensional representation $phi$ of $W$ over the finite field $F_2$ of two elements. The action of $phi(W)$ on $F_2^n$ by left multiplication is corresponding to a combinatorial structure extracted and generalized from Vogan diagrams. In each case W of types A, D and E, we determine the orbits of $F_2^n$ under the action of $phi(W)$, and find that the kernel of $phi$ is the center $Z(W)$ of $W.$
قيم البحث
اقرأ أيضاً
For the coinvariant rings of finite Coxeter groups of types other than H$_4$, we show that a homogeneous element of degree one is a strong Lefschetz element if and only if it is not fixed by any reflections. We also give the necessary and sufficient
condition for strong Lefschetz elements in the invariant subrings of the coinvariant rings of Weyl groups.
The core of a finite-dimensional modular representation $M$ of a finite group $G$ is its largest non-projective summand. We prove that the dimensions of the cores of $M^{otimes n}$ have algebraic Hilbert series when $M$ is Omega-algebraic, in the sen
se that the non-projective summands of $M^{otimes n}$ fall into finitely many orbits under the action of the syzygy operator $Omega$. Similarly, we prove that these dimension sequences are eventually linearly recursive when $M$ is what we term $Omega^{+}$-algebraic. This partially answers a conjecture by Benson and Symonds. Along the way, we also prove a number of auxiliary permanence results for linear recurrence under operations on multi-variable sequences.
In the 40s, Mayer introduced a construction of (simplicial) $p$-complex by using the unsigned boundary map and taking coefficients of chains modulo $p$. We look at such a $p$-complex associated to an $(n-1)$-simplex; in which case, this is also a $p$
-complex of representations of the symmetric group of rank $n$ - specifically, of permutation modules associated to two-row compositions. In this article, we calculate the so-called slash homology - a homology theory introduced by Khovanov and Qi - of such a $p$-complex. We show that every non-trivial slash homology group appears as an irreducible representation associated to two-row partitions, and how this calculation leads to a basis of these irreducible representations given by the so-called $p$-standard tableaux.
We define and study cocycles on a Coxeter group in each degree generalizing the sign function. When the Coxeter group is a Weyl group, we explain how the degree three cocycle arises naturally from geometry representation theory.
We classify all triples $(G,V,H)$ such that $SL_n(q)leq Gleq GL_n(q)$, $V$ is a representation of $G$ of dimension greater than one over an algebraically closed field $FF$ of characteristic coprime to $q$, and $H$ is a proper subgroup of $G$ such tha
t the restriction $Vdar_{H}$ is irreducible. This problem is a natural part of the Aschbacher-Scott program on maximal subgroups of finite classical groups.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
