34 citations · 195 across the 20 of their papers we have counts for
26 papers
Large products of double cosets for symmetric subgroups
Brendan Pawlowski
We consider the problem of classifying pairs such that where is a simple compact connected Lie group and is a symmetric subgroup. We give a nece…
Real 3-qubit gate decompositions via triality
Brendan Pawlowski
We show that any unimodular real 3-qubit gate can be expressed as the product of at most 14 CNOT gates plus single-qubit gates, improving on the bound of 16 CNOTs due to Wei and Di…
Introduction to the Cohomology of the Flag Variety
Sara C. Billey, Yibo Gao, Brendan Pawlowski
One hundred years ago, Hilbert gave a list of important open problems in mathematics. His 15th problem asked for the development of a rigorous calculus explaining Schubert's enumer…
Ideal transition systems
Eric Marberg, Brendan Pawlowski
We study an inductive method of computing initial ideals and Gröbner bases for families of ideals in a polynomial ring. This method starts from a given set of pairs where $…
Gröbner geometry for skew-symmetric matrix Schubert varieties
Eric Marberg, Brendan Pawlowski
Matrix Schubert varieties are the closures of the orbits of acting on all matrices, where is the group of invertible lower triangular matrices. Extendin…
The fraction of an -orbit on a hyperplane
Brendan Pawlowski
Huang, McKinnon, and Satriano conjectured that if has distinct coordinates and , then a hyperplane through the origin other than con…
Principal specializations of Schubert polynomials in classical types
Eric Marberg, Brendan Pawlowski
There is a remarkable formula for the principal specialization of a type A Schubert polynomial as a weighted sum over reduced words. Taking appropriate limits transforms this to an…
Involution pipe dreams
Zachary Hamaker, Eric Marberg, Brendan Pawlowski
Involution Schubert polynomials represent cohomology classes of -orbit closures in the complete flag variety, where is the orthogonal or symplectic group. We show they also…
Spanning subspace configurations and representation stability
Brendan Pawlowski, Eric Ramos, Brendon Rhoades
Let be a sequence of -vector spaces where carries an action of for each . {\em Representation stability} and {\em mult…
On some properties of symplectic Grothendieck polynomials
Eric Marberg, Brendan Pawlowski
Grothendieck polynomials, introduced by Lascoux and Schützenberger, are certain -theory representatives for Schubert varieties. Symplectic Grothendieck polynomials, described mo…
K-theory formulas for orthogonal and symplectic orbit closures
Eric Marberg, Brendan Pawlowski
The complex orthogonal and symplectic groups both act on the complete flag variety with finitely many orbits. We study two families of polynomials introduced by Wyser and Yong repr…
Universal graph Schubert varieties
Brendan Pawlowski
We consider the loci of invertible linear maps together with pairs of flags in such that the vario…
Pattern avoidance and quasisymmetric functions
Zachary Hamaker, Brendan Pawlowski, Bruce Sagan
Given a set of permutations Pi, let S_n(Pi) denote the set of permutations in the symmetric group S_n that avoid every element of Pi in the sense of pattern avoidance. Given a subs…
Reduced words for clans
Brian Burks, Brendan Pawlowski
Clans are combinatorial objects indexing the orbits of on the variety of flags in . This geometry leads to a partial or…
Stanley symmetric functions for signed involutions
Eric Marberg, Brendan Pawlowski
An involution in a Coxeter group has an associated set of involution words, a variation on reduced words. These words are saturated chains in a partial order first considered by Ri…
Chromatic symmetric functions via the group algebra of
Brendan Pawlowski
We prove some Schur positivity results for the chromatic symmetric function of a (hyper)graph , using connections to the group algebra of the symmetric group. The first su…
A flag variety for the Delta Conjecture
Brendan Pawlowski, Brendon Rhoades
The Delta Conjecture of Haglund, Remmel, and Wilson predicts the monomial expansion of the symmetric function , where are positive integers and $Δ'_{e_…
Fixed-point-free involutions and Schur P-positivity
Zachary Hamaker, Eric Marberg, Brendan Pawlowski
The orbits of the symplectic group acting on the type A flag variety are indexed by the fixed-point-free involutions in a finite symmetric group. The cohomology classes of the clos…
Schur P-positivity and involution Stanley symmetric functions
Zachary Hamaker, Eric Marberg, Brendan Pawlowski
The involution Stanley symmetric functions are the stable limits of the analogues of Schubert polynomials for the orbits of the orthogonal group in the flag variety. Th…
A representation-theoretic interpretation of positroid classes
Brendan Pawlowski
A positroid is the matroid of a real matrix with nonnegative maximal minors, a positroid variety is the closure of the locus of points in a complex Grassmannian whose matroid is a…
Transition formulas for involution Schubert polynomials
Zachary Hamaker, Eric Marberg, Brendan Pawlowski
The orbits of the orthogonal and symplectic groups on the flag variety are in bijection, respectively, with the involutions and fixed-point-free involutions in the symmetric group…
Involution words II: braid relations and atomic structures
Zachary Hamaker, Eric Marberg, Brendan Pawlowski
Involution words are variations of reduced words for twisted involutions in Coxeter groups. They arise naturally in the study of the Bruhat order, of certain Iwahori-Hecke algebra…
Involution words: counting problems and connections to Schubert calculus for symmetric orbit closures
Zachary Hamaker, Eric Marberg, Brendan Pawlowski
Involution words are variations of reduced words for involutions in Coxeter groups, first studied under the name of "admissible sequences" by Richardson and Springer. They are maxi…
Catalan matroid decompositions of certain positroids
Brendan Pawlowski
A positroid is the matroid of a matrix whose maximal minors are all nonnegative. Given a permutation in , the matroid of a generic matrix whose non-zero entri…