Tom Halverson
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View article: Monk rules for type $GL_n$ Macdonald polynomials
Monk rules for type $GL_n$ Macdonald polynomials Open
In this paper we give Monk rules for Macdonald polynomials which are analogous to the Monk rules for Schubert polynomials. These formulas are similar to the formulas given by Baratta (2008), but our method of derivation is to use Cherednik…
View article: Transition Matrices Between Young's Natural and Seminormal Representations
Transition Matrices Between Young's Natural and Seminormal Representations Open
We derive a formula for the entries in the change-of-basis matrix between Young's seminormal and natural representations of the symmetric group. These entries are determined as sums over weighted paths in the weak Bruhat graph on standard …
View article: Transition matrices between Young's natural and seminormal representations
Transition matrices between Young's natural and seminormal representations Open
We derive a formula for the entries in the change-of-basis matrix between Young's seminormal and natural representations of the symmetric group. These entries are determined as sums over weighted paths in the weak Bruhat graph on standard …
View article: Efficient simulation of so-called non-stoquastic superconducting flux\n circuits
Efficient simulation of so-called non-stoquastic superconducting flux\n circuits Open
There is a tremendous interest in fabricating superconducting flux circuits\nthat are nonstoquastic---i.e., have positive off-diagonal matrix elements---in\ntheir qubit representation, as these circuits are thought to be unsimulable by\ncl…
View article: Efficient simulation of so-called non-stoquastic superconducting flux circuits
Efficient simulation of so-called non-stoquastic superconducting flux circuits Open
There is a tremendous interest in fabricating superconducting flux circuits that are nonstoquastic---i.e., have positive off-diagonal matrix elements---in their qubit representation, as these circuits are thought to be unsimulable by class…
View article: McKay Centralizer Algebras
McKay Centralizer Algebras Open
For a finite subgroup G of the special unitary group SU2, we study the centralizer algebra Zk(G) = EndG(V⊗k) of G acting on the k-fold tensor product of its defining representation V = C2. The McKay corre- spondence relates the representat…
View article: Set-partition tableaux and representations of diagram algebras
Set-partition tableaux and representations of diagram algebras Open
The partition algebra is an associative algebra with a basis of set-partition diagrams and multiplication given by diagram concatenation. It contains as subalgebras a large class of diagram algebras including the Brauer, planar partition, …
View article: Equation of state and first principles prediction of the vibrational matrix shift of solid parahydrogen
Equation of state and first principles prediction of the vibrational matrix shift of solid parahydrogen Open
We generate the equation of state (EOS) of solid parahydrogen (para-H2) using a path-integral Monte Carlo (PIMC) simulation based on a highly accurate first-principles adiabatic hindered rotor potential energy curve for the para-H2 dimer. …
View article: Partition Algebras and the Invariant Theory of the Symmetric Group
Partition Algebras and the Invariant Theory of the Symmetric Group Open
The symmetric group $\mathsf{S}_n$ and the partition algebra $\mathsf{P}_k(n)$ centralize one another in their actions on the $k$-fold tensor power $\mathsf{M}_n^{\otimes k}$ of the $n$-dimensional permutation module $\mathsf{M}_n$ of $\ma…
View article: Tensor power multiplicities for symmetric and alternating groups and dimensions of irreducible modules for partition algebras
Tensor power multiplicities for symmetric and alternating groups and dimensions of irreducible modules for partition algebras Open
The partition algebra $\mathsf{P}_k(n)$ and the symmetric group $\mathsf{S}_n$ are in Schur-Weyl duality on the $k$-fold tensor power $\mathsf{M}_n^{\otimes k}$ of the permutation module $\mathsf{M}_n$ of $\mathsf{S}_n$, so there is a surj…
View article: McKay centralizer algebras
McKay centralizer algebras Open
For a finite subgroup $\\mathsf {G}$ of the special unitary group $\\mathsf {SU}_2$, we study the centralizer algebra $\\mathsf {Z}_k(\\mathsf {G}) = \\mathsf {End}_\\mathsf {G}(\\mathsf {V}^{\\otimes k})$ of $\\mathsf {G}$ acting on the $…
View article: Topological Data Analysis of Biological Aggregation Models
Topological Data Analysis of Biological Aggregation Models Open
We apply tools from topological data analysis to two mathematical models inspired by biological aggregations such as bird flocks, fish schools, and insect swarms. Our data consists of numerical simulation output from the models of Vicsek a…