اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدIrreducible decomposition and calculating of multiplicity of the symmetric and exterior powers representation of finite groups
195
0
0.0
(
0
)
تأليف
Tomoyuki Tamura
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
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 component of two representations of some representation by using a character theory of representation and a pre-lambda-ring, for example, the regular representation.
قيم البحث
اقرأ أيضاً
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.
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.
We investigate the structure and properties of an Artinian monomial complete intersection quotient $A(n,d)=mathbf{k} [x_{1}, ldots, x_{n}] big / (x_{1}^{d}, ldots, x_{n}^d)$. We construct explicit homogeneous bases of $A(n,d)$ that are compatible wit
h the $S_{n}$-module structure for $n=3$, all exponents $d ge 3$ and all homogeneous degrees $j ge 0$. Moreover, we derive the multiplicity formulas, both in recursive form and in closed form, for each irreducible component appearing in the $S_{3}$-module decomposition of homogeneous subspaces. 4, 5$.
Suppose that $G$ is a finite group and $H$ is a nilpotent subgroup of $G$. If a character of $H$ induces an irreducible character of $G$, then the generalized Fitting subgroup of $G$ is nilpotent.
We determine the multiplicities of irreducible summands in the symmetric and the exterior squares of hook representations of symmetric groups over an algebraically closed field of characteristic zero.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
