What is the Schur multiplier of a finite group?
In the book: J.H. Conway and R. T. Curtis and et al, Atlas of finite groups: Maximal Subgroups and Ordinary Characters for Simple Groups, Oxford University Press 1985. Page:xvii, “A central extension,...
View ArticleWhat is the Schur multiplier of a finite group?
In the book: J.H. Conway and R. T. Curtis and et al, Atlas of finite groups: Maximal Subgroups and Ordinary Characters for Simple Groups, Oxford University Press 1985. Page:xvii, “A central extension,...
View ArticleSchur function on unit circles
Define $ T^d$ as following $ $ T^d = \left\{(t_1,\cdots,t_d)\in\mathbb{C}^{d}\mid |t_i|= 1 \mbox{ for all } i\right\} $ $ For any partition $ \lambda\vdash n$ ,The Schur function is defined $ $...
View ArticleReference for Schur multiplier identity
Let $ G$ be a finite group and $ H$ a normal subgroup of $ G$ . I recently stumbled upon the following identity for the Schur multiplier of $ G/H$ : $ $ \operatorname{H}_2(G/H,\mathbb{Z}) \cong...
View ArticleSchur index of a representation and its divisors
We fix following objects: (1) $ G$ is a finite group. (2) $ \chi$ is complex irreducible character of $ G$ . (3) $ m$ is the Schur index of $ \chi$ w.r.t. the rational field $ \mathbb{Q}$ . (4) All...
View ArticleConnection between Schur multipliers in representation theory and functional...
I was wondering if there is any connection between two things called Schur multipliers or is it just a coincidence? Namely, in representation/group theory the Schur multiplier of a group $ G$ is its...
View ArticleSchur norm of weighted Cauchy matrix
The Schur norm of a matrix $ A$ is defined to be $ \|A\|_S=\max\{\|A\circ X\|: \|X\|\leq 1\}$ , where $ \|\cdot \|$ is the operator norm of a matrix, i.e., the largest singular value. Let $...
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