Pioneers of Representation Theory: Frobenius, Burnside, Schur, and Brauer
نویسندگان
چکیده
منابع مشابه
The Brauer group of Burnside rings
The Brauer group of a commutative ring is an important invariant of a commutative ring, a common journeyman to the group of units and the Picard group. Burnside rings of finite groups play an important rôle in representation theory, and their groups of units and Picard groups have been studied extensively. In this short note, we completely determine the Brauer groups of Burnside rings: they van...
متن کاملBurnside-Brauer Theorem for Table Algebras
In the character theory of finite groups the Burnside-Brauer Theorem is a wellknown result which deals with products of characters in finite groups. In this paper, we first define the character products for table algebras and then by observing the relationship between the characters of a table algebra and the characters of its quotient, we provide a condition in which the products of characters...
متن کاملBrauer Algebras, Symplectic Schur Algebras and Schur-weyl Duality
In this paper we prove the Schur-Weyl duality between the symplectic group and the Brauer algebra over an arbitrary infinite field K. We show that the natural homomorphism from the Brauer algebra Bn(−2m) to the endomorphism algebra of the tensor space (K2m)⊗n as a module over the symplectic similitude group GSp2m(K) (or equivalently, as a module over the symplectic group Sp2m(K)) is always surj...
متن کاملBurnside-Brauer Theorem and Character Products in Table Algebras
In this paper, we first show that the irreducible characters of a quotient table algebra modulo a normal closed subset can be viewed as the irreducible characters of the table algebra itself. Furthermore, we define the character products for table algebras and give a condition in which the products of two characters are characters. Thereafter, as a main result we state and prove the Burnside-Br...
متن کاملOn the Representation Theory of Partial Brauer Algebras
In this paper we study the partial Brauer C-algebras Rn(δ, δ ), where n ∈ N and δ, δ ∈ C. We show that these algebras are generically semisimple, construct the Specht modules and determine the Specht module restriction rules for the restriction Rn−1 →֒ Rn. We also determine the corresponding decomposition matrix, and the Cartan decomposition matrix.
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ژورنال
عنوان ژورنال: Historia Mathematica
سال: 2003
ISSN: 0315-0860
DOI: 10.1016/s0315-0860(02)00012-5