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J. Losonczy

Publications and source records attributed to J. Losonczy.

6 recordsLinked to original sources
arXiv2004

Schubert varieties and free braidedness

We give a simple necessary and sufficient condition for a Schubert variety $X_w$ to be smooth when $w$ is a freely braided element of a simply laced Weyl group; such elements were introduced by the authors in a previous work (math.CO/0301104). This generalizes in one direction a result of Fan concerning varieties indexed by short-braid avoiding elements. We also derive generating functions for the freely braided elements that index smooth Schubert varieties. All results are stated and proved only for the simply laced case.

math.CO↗
arXiv2003

Freely braided elements in Coxeter groups, II

We continue the study of freely braided elements of simply laced Coxeter groups, which we introduced in a previous work (math.CO/0301104). A known upper bound for the number of commutation classes of reduced expressions for an element of a simply laced Coxeter group is shown to be achieved only when the element is freely braided; this establishes the converse direction of a previous result. It is also shown that a simply laced Coxeter group has finitely many freely braided elements if and only if it has finitely many fully commutative elements.

math.CO↗
arXiv2003

Freely braided elements in Coxeter groups

We introduce a notion of "freely braided element" for simply laced Coxeter groups. We show that an arbitrary group element $w$ has at most $2^{N(w)}$ commutation classes of reduced expressions, where $N(w)$ is a certain statistic defined in terms of the positive roots made negative by $w$. This bound is achieved if $w$ is freely braided. In the type $A$ setting, we show that the bound is achieved only for freely braided $w$.

math.CO↗
arXiv2001

Fully commutative Kazhdan-Lusztig cells

We investigate the compatibility of the set of fully commutative elements of a Coxeter group with the various types of Kazhdan-Lusztig cells using a canonical basis for a generalized version of the Temperley-Lieb algebra.

math.QA↗
arXiv1999

Canonical Bases for Hecke Algebra Quotients

We establish the existence of an IC basis for the generalized Temperley--Lieb algebra associated to a Coxeter system of arbitrary type. We determine this basis explicitly in the case where the Coxeter system is simply laced and the algebra is finite dimensional.

math.QA↗