On some extensions of p-restricted completely splittable GL(n)-modules

نویسنده

  • Vladimir Shchigolev
چکیده

In this paper, we calculate the space ExtGL(n)(Ln(λ), Ln(μ)), where GL(n) is the general linear group of degree n over an algebraically closed field of positive characteristic, Ln(λ) and Ln(μ) are rational irreducible GL(n)-modules with highest weights λ and μ respectively, the restriction of Ln(λ) to any Levi subgroup of GL(n) is semisimple, λ is a p-restricted weight and μ does not strictly dominate λ.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

On extensions and branching rules for modules close to completely splittable

We describe the modules Dλ↓Σn−1 and D λ↑n+1 for certain simple KΣn-modules (completely splittable and some close to) D, where K is a field of characteristic p > 0 and Σn is the symmetric group of degree n. This result is based on an upper bound of the dimensions of the Ext-spaces between some simple modules.

متن کامل

The Ext-quiver for completely splittable representations of the symmetric group

Kleshchev has recently [7] classi®ed those modules for the symmetric group which have semisimple restriction to any Young subgroup. We determine Ext K Sd …D ;D m† where D l and D m are K Sd -modules of this type, called completely splittable. As a corollary of this and recent work of Kleshchev and Nakano, we can determine ExtGL n…K†……L…l†;L…m†† for certain simple GLn…K†-modules L…l† and L…m†. 1...

متن کامل

On simple modules for the restricted Lie superalgebra gl(m|n)

In this paper, we study the simple modules for the restricted Lie superalgebra gl(m|n). A condition for the simplicity of the induced modules is given, and an analogue of Kac-Weisfeiler theorem is proved. Mathematics Subject Classification (2000): 17B50; 17B10.

متن کامل

On Twin--Good Rings

In this paper, we investigate various kinds of extensions of twin-good rings. Moreover, we prove that every element of an abelian neat ring R is twin-good if and only if R has no factor ring isomorphic to‌ Z2  or Z3. The main result of [24] states some conditions that any right self-injective ring R is twin-good. We extend this result to any regular Baer ring R by proving that every elemen...

متن کامل

Incidence Homology of Finite Projective Spaces

Let F be the finite field of q elements and let P(n, q) be the projective space of dimension n−1 over F. We construct a family H k,i of combinatorial homology modules associated to P(n, q) over a coefficient field F field of characteristic p0 > 0 co-prime to q. As FGL(n, q) -representations the modules are obtained from the permutation action of GL(n, q) on the subspaces of F. We prove a branch...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2007