اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدExterior powers of the reflection representation in Springer theory
172
0
0.0
(
0
)
تأليف
Eric Sommers
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We give a proof of a conjecture of Lehrer and Shoji regarding the occurrences of the exterior powers of the reflection representation in the cohomology of Springer fibers. The actual theorem proved is a slight extension of the original conjecture to all nilpotent orbits and also takes into account the action of the component group. The method is to use Shojis approach to the orthogonality formulas for Green functions to relate the symmetric algebra to a sum over Green functions. In the second part of the paper we give an explanation of the appearance of the Orlik-Solomon exponents using a result from rational Cherednik algebras.
قيم البحث
اقرأ أيضاً
In this paper we consider symmetric powers representation and exterior powers representation of finite groups, which generated by the representation which has finite dimension over the complex field. We calculate the multiplicity of irreducible compo
nent of two representations of some representation by using a character theory of representation and a pre-lambda-ring, for example, the regular representation.
For given representation of finite groups on a finite dimension complex vector space, we can define exterior powers of representations. In 1973, Knutson found one of methods of calculating the character of exterior powers of representations with prop
erties of $lambda$-rings. In this paper, we base this result of Knutson, and relate characters and elements of necklace rings, which were introduced by N.Metropolis and G-C.Rota in 1983, via a generating function of the character of exterior powers of representations. We focus on integer-valued characters and discuss a relation between integer-valued characters and element of necklace rings which has finite support and is contained in some images of truncated operations.
A sequence of $S_n$-representations ${V_n}$ is said to be uniformly representation stable if the decomposition of $V_n = bigoplus_{mu} c_{mu,n} V(mu)_n$ into irreducible representations is independent of $n$ for each $mu$---that is, the multiplicitie
s $c_{mu,n}$ are eventually independent of $n$ for each $mu$. Church-Ellenberg-Farb proved that the cohomology of flag varieties (the so-called diagonal coinvariant algebra) is uniformly representation stable. We generalize their result from flag varieties to all Springer fibers. More precisely, we show that for any increasing subsequence of Young diagrams, the corresponding sequence of Springer representations form a graded co-FI-module of finite type (in the sense of Church-Ellenberg-Farb). We also explore some combinatorial consequences of this stability.
These myh lectures at the Park City conference in 1998.
Let $K$ be a field and $V$ and $W$ be $K$-vector spaces of dimension $m$ and $n$. Let $phi$ be the canonical map from $Hom(V,W)$ to $Hom(wedge^t V,wedge^t W)$. We investigate the Zariski closure $X_t$ of the image $Y_t$ of $phi$. In the case $t=min(m
,n)$, $Y_t=X_t$ is the cone over a Grassmannian, but $X_t$ is larger than $Y_t$ for $1<t<min(m,n)$. We analyze the $G=GL(V)timesGL(W)$-orbits in $X_t$ via the corresponding $G$-stable prime ideals. It turns out that they are classified by two numerical invariants, one of which is the rank and the other a related invariant that we call small rank. Surprisingly, the orbits in $X_tsetminus Y_t$ arise from the images $Y_u$ for $u<t$ and simple algebraic operations. In the last section we determine the singular locus of $X_t$. Apart from well-understood exceptional cases, it is formed by the elements of rank $le 1$ in $Y_t$.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
