Embedding the Flag Representation in Divided Powers
نویسنده
چکیده
A generalization of a theorem of Crabb and Hubbuck concerning the embedding of flag representations in divided powers is given, working over an arbitrary finite field F, using the category of functors from finite-dimensional F-vector spaces to F-vector spaces.
منابع مشابه
A remark on asymptotic enumeration of highest weights in tensor powers of a representation
We consider the semigroup $S$ of highest weights appearing in tensor powers $V^{otimes k}$ of a finite dimensional representation $V$ of a connected reductive group. We describe the cone generated by $S$ as the cone over the weight polytope of $V$ intersected with the positive Weyl chamber. From this we get a description for the asymptotic of the number of highest weights appearing in $V^{otime...
متن کاملA New Document Embedding Method for News Classification
Abstract- Text classification is one of the main tasks of natural language processing (NLP). In this task, documents are classified into pre-defined categories. There is lots of news spreading on the web. A text classifier can categorize news automatically and this facilitates and accelerates access to the news. The first step in text classification is to represent documents in a suitable way t...
متن کاملA Joint Semantic Vector Representation Model for Text Clustering and Classification
Text clustering and classification are two main tasks of text mining. Feature selection plays the key role in the quality of the clustering and classification results. Although word-based features such as term frequency-inverse document frequency (TF-IDF) vectors have been widely used in different applications, their shortcoming in capturing semantic concepts of text motivated researches to use...
متن کاملDetecting Overlapping Communities in Social Networks using Deep Learning
In network analysis, a community is typically considered of as a group of nodes with a great density of edges among themselves and a low density of edges relative to other network parts. Detecting a community structure is important in any network analysis task, especially for revealing patterns between specified nodes. There is a variety of approaches presented in the literature for overlapping...
متن کاملIntegral Intertwining Operators and Complex Powers of Differential (q−Difference) Operators
We study a family of modules over Kac-Moody algebras realized in multi-valued functions on a flag manifold and find integral representations for intertwining operators acting on these modules. These intertwiners are related to some expressions involving complex powers of Lie algebra generators. When applied to affine Lie algebras, these expressions give integral formulas for correlation functio...
متن کامل