[图书][B] Lie groups, Lie algebras, and representations
BC Hall, BC Hall - 2013 - Springer
An important concept in physics is that of symmetry, whether it be rotational symmetry for
many physical systems or Lorentz symmetry in relativistic systems. In many cases, the group …
many physical systems or Lorentz symmetry in relativistic systems. In many cases, the group …
Kostant partitions functions and flow polytopes
W Baldoni, M Vergne - Transformation Groups, 2008 - Springer
This paper discusses volumes and Ehrhart polynomials in the context of flow polytopes. The
general approach that studies these functions via rational functions with poles on …
general approach that studies these functions via rational functions with poles on …
Multipartite quantum states and their marginals
M Walter - arXiv preprint arXiv:1410.6820, 2014 - arxiv.org
Subsystems of composite quantum systems are described by reduced density matrices, or
quantum marginals. Important physical properties often do not depend on the whole wave …
quantum marginals. Important physical properties often do not depend on the whole wave …
Computing multiplicities of Lie group representations
For fixed compact connected Lie groups H⊆ G, we provide a polynomial time algorithm to
compute the multiplicity of a given irreducible representation of H in the restriction of an …
compute the multiplicity of a given irreducible representation of H in the restriction of an …
Applications of equivariant cohomology
M Vergne - arXiv preprint math/0607389, 2006 - arxiv.org
We will discuss the equivariant cohomology of a manifold endowed with the action of a Lie
group. Localization formulae for equivariant integrals are explained by a vanishing theorem …
group. Localization formulae for equivariant integrals are explained by a vanishing theorem …
On the computation of Clebsch–Gordan coefficients and the dilation effect
JA De Loera, TB McAllister - Experimental Mathematics, 2006 - Taylor & Francis
We investigate the problem of computing tensor product multiplicities for complex
semisimple Lie algebras. Even though computing these numbers is# P-hard in general, we …
semisimple Lie algebras. Even though computing these numbers is# P-hard in general, we …
Flow polytopes of signed graphs and the Kostant partition function
K Mészáros, AH Morales - International Mathematics Research …, 2015 - ieeexplore.ieee.org
We establish the relationship between volumes of flow polytopes associated to signed
graphs and the Kostant partition function. A special case of this relationship, namely, when …
graphs and the Kostant partition function. A special case of this relationship, namely, when …
Root cones and the resonance arrangement
SC Gutekunst, K Mészáros, TK Petersen - arXiv preprint arXiv:1903.06595, 2019 - arxiv.org
We study the connection between triangulations of a type $ A $ root polytope and the
resonance arrangement, a hyperplane arrangement that shows up in a surprising number of …
resonance arrangement, a hyperplane arrangement that shows up in a surprising number of …
The polytope of Tesler matrices
K Mészáros, AH Morales, B Rhoades - Selecta Mathematica, 2017 - Springer
We introduce the Tesler polytope Tes _n (a) Tes n (a), whose integer points are the Tesler
matrices of size n with hook sums a_1, a_2, ..., a_n ∈ Z _ ≥ 0 a 1, a 2,…, an∈ Z≥ 0. We …
matrices of size n with hook sums a_1, a_2, ..., a_n ∈ Z _ ≥ 0 a 1, a 2,…, an∈ Z≥ 0. We …
Geometric complexity theory VI: the flip via saturated and positive integer programming in representation theory and algebraic geometry
KD Mulmuley - arXiv preprint arXiv:0704.0229, 2007 - arxiv.org
This article belongs to a series on geometric complexity theory (GCT), an approach to the P
vs. NP and related problems through algebraic geometry and representation theory. The …
vs. NP and related problems through algebraic geometry and representation theory. The …