- journal articles metadata
European Mathematical Society Publishing House
2024-03-19 12:44:08
2
https://www.ems-ph.org/meta/jmeta-stream.php?jrn=JCA&vol=1&iss=4&update_since=2024-03-19
Journal of Combinatorial Algebra
J. Comb. Algebra
JCA
2415-6302
2415-6310
Combinatorics
Group theory and generalizations
10.4171/JCA
http://www.ems-ph.org/doi/10.4171/JCA
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
1
2017
4
Multifraction reduction III: The case of interval monoids
Patrick
Dehornoy
Université de Caen, France
Friedrich
Wehrung
Université de Caen, France
Poset, intervalmonoid, gcd-monoid, enveloping group, word problem,multifraction, reduction, embeddability, semi-convergence, circuit, zigzag
We investigate gcd-monoids, which are cancellative monoids in which any two elements admit a left and a right gcd, and the associated reduction of multifractions (arXiv:1606.08991 and 1606.08995), a general approach to the word problemfor the enveloping group. Here we consider the particular case of interval monoids associated with finite posets. In this way, we construct gcd-monoids, in which reduction of multifractions has prescribed properties not yet known to be compatible: semi-convergence of reductionwithout convergence, semi-convergence up to some level but not beyond, non-embeddability into the enveloping group (a strong negation of semi-convergence).
Order, lattices, ordered algebraic structures
Category theory; homological algebra
Group theory and generalizations
Computer science
341
370
10.4171/JCA/1-4-1
http://www.ems-ph.org/doi/10.4171/JCA/1-4-1
Young tableaux and representations of Hecke algebras of type ADE
Loïc
Poulain d'Andecy
Université de Reims Champagne-Ardenne, France
Hecke algebras, Weyl groups, simply-laced root systems, affine Hecke algebras, Jucys–Murphy elements, skew partitions, Young tableaux, seminormal representations, calibrated representations
We introduce and study some affine Hecke algebras of type ADE, generalising the affine Hecke algebras of GL. We construct irreducible calibrated representations and describe the calibrated spectrum. This is done in terms of new families of combinatorial objects equipped with actions of the corresponding Weyl groups. These objects are built from and generalise the usual standard Young tableaux, and are controlled by the considered affine Hecke algebras. By restriction and limiting procedure, we obtain several combinatorial models for representations of finite Hecke algebras and Weyl groups of type ADE. Representations are constructed by explicit formulas, in a seminormal form.
Group theory and generalizations
Combinatorics
371
423
10.4171/JCA/1-4-2
http://www.ems-ph.org/doi/10.4171/JCA/1-4-2