Browsing School of Mathematics, Statistics and Applied Mathematics by Author "Pfeiffer, Götz"
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An algorithm for the unit group of the Burnside ring of a finite group
Boltje, Robert; Pfeiffer, Götz (Cambridge University Press, 200701)In this note we present an algorithm for the construction of the unit group of the Burnside ring Ω(G) of a finite group G from a list of representatives of the conjugacy classes of subgroups of G. 
The BMR freeness conjecture for the 2reflection groups
Marin, Ivan; Pfeiffer, Götz (American Mathematical Society, 20161012)We prove the freeness conjecture of Broue, Malle and Rouquier for the Hecke algebras associated to the primitive complex 2reflection groups with a single conjugacy class of reflections. 
Cohomology of Coxeter arrangements and Solomon's descent algebra
Douglass, J. Matthew; Pfeiffer, Götz; Röhrle, Gerhard (American Mathematical Society, 20140619)We refine a conjecture by Lehrer and Solomon on the structure of the OrlikSolomon algebra of a finite Coxeter group W and relate it to the descent algebra of W. As a result, we claim that both the group algebra of W and ... 
Computations for Coxeter arrangements and Solomon's descent algebra II: Groups of rank five and six
Bishop, Marcus; Douglass, J. Matthew; Pfeiffer, Götz; Röhrle, Gerhard (Elsevier, 20130108)In recent papers we have refined a conjecture of Lehrer and Solomon expressing the character of a finite Coxeter group W acting on the graded components of its OrlikSolomon algebra as a sum of characters induced from ... 
Computations for Coxeter arrangements and Solomon's descent algebra III: Groups of rank seven and eight
Bishop, Marcus; Douglass, J. Matthew; Pfeiffer, Götz; Röhrle, Gerhard (Elsevier, 20141106)In this paper we extend the computations in parts I and II of this series of papers and complete the proof of a conjecture of Lehrer and Solomon expressing the character of a finite Coxeter group W acting on the pth graded ... 
Computations for Coxeter arrangements and Solomon's descent algebra: Groups of rank three and four
Bishop, Marcus; Douglass, J. Matthew; Pfeiffer, Götz; Röhrle, Gerhard (Elsevier, 20120603)In recent papers we have refined a conjecture of Lehrer and Solomon expressing the characters of a finite Coxeter group W afforded by the homogeneous components of its OrlikSolomon algebra as sums of characters induced ... 
Computing the table of marks of a cyclic extension
Naughton, L.; Pfeiffer, Götz (American Mathematical Society, 20120224)The subgroup pattern of a finite group C is the table of marks of G together with a list of representatives of the conjugacy classes of subgroups of G. In this article we present an algorithm for the computation of the ... 
An inductive approach to Coxeter arrangements and Solomon's descent algebra
Dolan, J. Matthew; Pfeiffer, Götz; Röhrle, Gerhard (Springer Verlag, 20120720)In our recent paper (Douglass et al. arXiv: 1101.2075 (2011)), we claimed that both the group algebra of a finite Coxeter group W as well as the OrlikSolomon algebra of W can be decomposed into a sum of induced onedimensional ... 
A note on element centralizers in finite Coxeter groups
Konvalinka, Matjaž; Pfeiffer, Götz; Röver, Claas E. (De Gruyter, 20110829)The normalizer NW(WJ) of a standard parabolic subgroup WJ of a finite Coxeter group W splits over the parabolic subgroup with complement NJ consisting of certain minimal length coset representatives of WJ in W. In ... 
On reflection subgroups of finite Coxeter groups
Douglass, J. Matthew; Pfeiffer, Götz; Röhrle, Gerhard (Taylor & Francis, 20130614)Let W be a finite Coxeter group. We classify the reflection subgroups of W up to conjugacy and give necessary and sufficient conditions for the map that assigns to a reflection subgroup R of W the conjugacy class of its ... 
On the complexity of multiplication in the IwahoriHecke algebra of the symmetric group
Niemeyer, Alice C.; Pfeiffer, Götz; Praeger, Cheryl E. (Elsevier, 20160912)We present new efficient data structures for elements of Coxeter groups of type Am and their associated Iwahori Hecke algebras H(A(m)). Usually, elements of H(A(m)) are represented as simple coefficient list of length M = ... 
On the quiver presentation of the descent algebra of the symmetric group
Bishop, Marcus; Pfeiffer, Götz (Elsevier, 20130318)We describe a presentation of the descent algebra of the symmetric group G(n) as a quiver with relations. This presentation arises from a new construction of the descent algebra as a homomorphic image of an algebra of ... 
On the table of marks of a direct product of finite groups
Masterson, Brendan; Pfeiffer, Götz (Elsevier, 20171228)We present a method for computing the table of marks of a direct product of finite groups. In contrast to the character table of a direct product of two finite groups, its table of marks is not simply the Kronecker product ... 
A quiver presentation for Solomon's descent algebra
Pfeiffer, Götz (Elsvier, 2009)The descent algebra S(W) is a subalgebra of the group algebra of a finite Coxeter group W, which supports a homomorphism with nilpotent kernel and commutative image in the character ring of W. Thus S(W) is a basic algebra, ...