Theorem of Poincare-Birkhoff-Witt, logarithm and symmetric group representations of degrees equal to stirling numbers

1986 ◽  
pp. 267-284 ◽  
Author(s):  
Christophe Reutenauer
Keyword(s):  
Symmetric Group ◽  
Stirling Numbers ◽  
Group Representations ◽  
Symmetric Group Representations

scholarly journals Symmetric group representations andZ

2018 ◽  
Vol 356 (1) ◽  
pp. 1-4
Author(s):  
Anshul Adve ◽  
Alexander Yong
Keyword(s):  
Symmetric Group ◽  
Group Representations ◽  
Symmetric Group Representations

Products and Plethysms of Characters with Orthogonal, Symplectic and Symmetric Groups

1958 ◽  
Vol 10 ◽  
pp. 17-32 ◽  
Author(s):  
D. E. Littlewood
Keyword(s):  
Symmetric Group ◽  
Kronecker Product ◽  
Symmetric Groups ◽  
Group Representations ◽  
Symmetric Group Representations

Murnaghan (9) has proposed the following method of analyzing the Kronecker product of two symmetric group representations. If (λ) = (λ1, λ2, … , λi) is a partition of p, the representation of the symmetric group on n symbols corresponding to the partition (n — p, λ1 , … , λi) is denoted by [λ] and is said to be of depth p. If [λ] is of depth p and [μ] of depth q, then the terms in the Kronecker product [λ] X [μ] of depth p + q are terms which correspond to the terms in the product of S-functions {λ} {μ}).

scholarly journals On signed Young permutation modules and signed p-Kostka numbers

2017 ◽  
Vol 20 (4) ◽  
Author(s):  
Eugenio Giannelli ◽  
Kay Jin Lim ◽  
William O’Donovan ◽  
Mark Wildon
Keyword(s):  
Symmetric Group ◽  
Group Representations ◽  
Kostka Numbers ◽  
Basic Facts ◽  
Symmetric Group Representations

AbstractWe prove the existence and main properties of signed Young modules for the symmetric group, using only basic facts about symmetric group representations and the Broué correspondence. We then prove new reduction theorems for the signed

HOPF ALGEBRAS OF SYMMETRIC FUNCTIONS AND TENSOR PRODUCTS OF SYMMETRIC GROUP REPRESENTATIONS

1991 ◽  
Vol 01 (02) ◽  
pp. 207-221 ◽  
Author(s):  
JEAN-YVES THIBON
Keyword(s):  
Hopf Algebra ◽  
Tensor Product ◽  
Symmetric Group ◽  
Hopf Algebras ◽  
Symmetric Functions ◽  
Tensor Products ◽  
Ring Structure ◽  
Algebra Structure ◽  
Group Representations ◽  
Symmetric Group Representations

The Hopf algebra structure of the ring of symmetric functions is used to prove a new identity for the internal product, i.e., the operation corresponding to the tensor product of symmetric group representations. From this identity, or by similar techniques which can also involve the λ-ring structure, we derive easy proofs of most known results about this operation. Some of these results are generalized.

scholarly journals Congruences induced by transitive representations of inverse semigroups

1987 ◽  
Vol 29 (1) ◽  
pp. 21-40 ◽  
Author(s):  
Mario Petrich ◽  
Stuart Rankin
Keyword(s):  
General Theory ◽  
Inverse Semigroup ◽  
Symmetric Group ◽  
Transitive Group ◽  
Inverse Semigroups ◽  
Group Representations ◽  
Symmetric Inverse Semigroup ◽  
The Right ◽  
Special Case

Transitive group representations have their analogue for inverse semigroups as discovered by Schein [7]. The right cosets in the group case find their counterpart in the right ω-cosets and the symmetric inverse semigroup plays the role of the symmetric group. The general theory developed by Schein admits a special case discovered independently by Ponizovskiǐ [4] and Reilly [5]. For a discussion of this topic, see [1, §7.3] and [2, Chapter IV].

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