6 papers
Conjugacy classes of regular integer matrices
Claus Hertling, Khadija Larabi
This paper is devoted to the theory of -conjugacy classes of regular integer matrices and related commutative semigroups. Such a matrix is $GL_n({\ma…
Semigroups from full lattices in commutative -algebras
Claus Hertling, Khadija Larabi
The full lattices in a finite dimensional commutative -algebra form a commutative semigroup. In the case of an algebraic number field the top part of a certain quotien…
Characterization of distinguished matrices of isolated hypersurface singularities through their spectral numbers
Sven Balnojan, Claus Hertling
Isolated hypersurface singularities come equipped with distinguished bases of their Milnor lattices and with upper triangular integral matrices, which are called here distinguished…
Odd vanishing cycles in cyclotomic fields
Claus Hertling, Khadija Larabi
A cusp of a Hecke group has two natural lifts to the ring of integers of a cyclotomic field. These lifts are called here odd vanishing cycles. All lifts of all cusps together…
Unimodular bilinear lattices, automorphism groups, vanishing cycles, monodromy groups, distinguished bases, braid group actions and moduli spaces from upper triangular matrices
Claus Hertling, Khadija Larabi
This monograph starts with an upper triangular matrix with integer entries and 1's on the diagonal. It develops from this a spectrum of structures, which appear in different contex…
Reduced and nonreduced presentations of Weyl group elements
Sven Balnojan, Claus Hertling
This paper is a sequel to work of Dynkin on subroot lattices of root lattices and to work of Carter on presentations of Weyl group elements as products of reflections. The quotient…