On Cartan matrices and lower defect groups for covering groups of symmetric groups
نویسندگان
چکیده
منابع مشابه
On Cartan matrices and lower defect groups for covering groups of symmetric groups
We determine the elementary divisors of the Cartan matrices of spin p-blocks of the covering groups of the symmetric groups when p is an odd prime. As a consequence, we also compute the determinants of these Cartan matrices, and in particular we confirm a conjecture by Brundan and Kleshchev that these determinants depend only on the weight but not on the sign of the block. The main purpose of t...
متن کاملA Note on Cartan Matrices for Symmetric Groups
Using generating functions a very simple explicit formula for the determinants of the p-Cartan matrices of symmetric groups is given. Our method works also when p is a composite number.
متن کاملCritical Groups of Mckay-cartan Matrices
This thesis investigates the critical groups of McKay-Cartan matrices, a certain type of avalanche-finite matrix associated to a faithful representation γ of a finite group G. It computes the order of the critical group in terms of the character values of γ, and gives some restrictions on its subgroup structure. In addition, the existence of a certain Smith normal form over Z[t] is shown to imp...
متن کاملSymmetric Groups and Random Matrices
The convolution of indicators of two conjugacy classes on the symmetric group Sq is usually a complicated linear combination of indicators of many conjugacy classes. Similarly, a product of the moments of the Jucys–Murphy element involves many conjugacy classes with complicated coefficients. In this article we consider a combinatorial setup which allows us to manipulate such products easily and...
متن کاملcommuting and non -commuting graphs of finit groups
فرض کنیمg یک گروه غیر آبلی متناهی باشد . گراف جابجایی g که با نماد نمایش داده می شود ،گرافی است ساده با مجموعه رئوس که در آن دو راس با یک یال به هم وصل می شوند اگر و تنها اگر . مکمل گراف جابجایی g راگراف نا جابجایی g می نامیم.و با نماد نشان می دهیم. گرافهای جابجایی و ناجابجایی یک گروه متناهی ،اولین بار توسطاردوش1 مطرح گردید ،ولی در سالهای اخیر به طور مفصل در مورد بحث و بررسی قرار گرفتند . در ،م...
15 صفحه اولذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2005
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-05-03809-2