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In this paper we study the determinant of irreducible representations of the generalized symmetric groups $\mathbb{Z}_r \wr S_n$. We give an explicit formula to compute the determinant of an irreducible representation of $\mathbb{Z}_r \wr S_n$. Recently, several authors have characterized and counted the number of irreducible representations of a given finite group with nontrivial determinant. Motivated by these results, for given integer $n$, $r$ an odd prime and $\zeta$ a nontrivial multiplicative character of $\mathbb{Z}_r \wr S_n$ with $n

Young's orthogonal basis is a classical basis for an irreducible representation of a symmetric group. This basis happens to be a Gelfand-Tsetlin basis for the chain of symmetric groups. It is well-known that the chain of alternating groups, just like the chain of symmetric groups, has multiplicity-free restrictions for irreducible representations. Therefore each irreducible representation of an alternating group also admits Gelfand-Tsetlin bases. Moreover, each such representation is either the restriction of, or a subrepresentation of, the restriction of an irreducible representation of a symmetric group. In this article, we describe a recursive algorithm to write down the expansion of each Gelfand-Tsetlin basis vector for an irreducible representation of an alternating group in terms of Young's orthogonal basis of the ambient representation of the symmetric group. This algorithm is implemented with the Sage Mathematical Software., Comment: 17 pages, 2 figures; version accepted for publication

The aim of Named Entity Recognition (NER) is to identify references of named entities in unstructured documents, and to classify them into pre-defined semantic categories. NER often aids from added background knowledge in the form of gazetteers. However using such a collection does not deal with name variants and cannot resolve ambiguities associated in identifying the entities in context and associating them with predefined categories. We present a semi-supervised NER approach that starts with identifying named entities with a small set of training data. Using the identified named entities, the word and the context features are used to define the pattern. This pattern of each named entity category is used as a seed pattern to identify the named entities in the test set. Pattern scoring and tuple value score enables the generation of the new patterns to identify the named entity categories. We have evaluated the proposed system for English language with the dataset of tagged (IEER) and untagged (CoNLL 2003) named entity corpus and for Tamil language with the documents from the FIRE corpus and yield an average f-measure of 75% for both the languages., Comment: 13 pages, 2 figures, 5 tables

Issai Schur, in his doctoral thesis (1901) introduced the Schur algebra to study the polynomial representation theory of the general linear group. He described a basis of this algebra and structure constants. Later, Miguel Mendez (2001) gave a graph-theoretic description of Schur's basis and computed the structure constants. In this presentation, we will give a new graphic interpretation of the basis of Schur algebra and use it to give a description of the structure constants which is equivalent to the one given by Mendez., Comment: 5 pages, appeared in Electronic booklet of Proceedings of International Congress of Women Mathematicians (ICWM 2014). 2014 ICWM Poster Abstract Number: 20140020