We find a minimal set of generators for the coordinate ring Calogero-Moser space ${\boldsymbol {\mathcal {C}}}_{\boldsymbol {3}}$ and algebraic relations among them explicitly. give new presentation algebra 3×3 invariant matrices involving defining ${\mathbb {C}}[\boldsymbol {C}}_{\boldsymbol {3}}]$ . Furthermore, we an explicit description GL3-invariant commuting variety its orbits under actio...

Abstract We study a quantum analogue of the 2-Wasserstein distance as measure proximity on set ? N density matrices dimension N . show that such (semi-)distances do not induce Riemannian metrics tangent bundle ...

For two positive integers m and n, we let Pn be the open convex cone in R consisting of positive definite n × n real symmetric matrices and let R be the set of all m×n real matrices. In this article, we investigate differential operators on the non-reductive manifold Pn × R (m,n) that are invariant under the natural action of the semidirect product group GL(n,R)⋉R on the MinkowskiEuclid space P...

We characterize the exposed faces of convex sets C of symmetric matrices, invariant under orthogonal similarity (U T CU = C for all orthogonal U). Such sets C are exactly those determined by eigenvalue constraints: typical examples are the positive semideenite cone, and unit balls of common matrix norms. The set D of all diagonal matrices in C is known to be convex if and only if C is, and D is...

In this paper, we investigate the concept of topological stationary for locally compact semigroups. In [4], T. Mitchell proved that a semigroup S is right stationary if and only if m(S) has a left Invariant mean. In this case, the set of values ?(f) where ? runs over all left invariant means on m(S) coincides with the set of constants in the weak* closed convex hull of right translates of f. Th...

In fermion mixing phenomenology, the matrix of moduli squared, P = (|U |2), is well-known to carry essentially the same information as the complex mixing matrix U itself, but with the advantage of being phase-convention independent. The matrix K (analogous to the Jarlskog CP -invariant J) formed from the real parts of the mixing matrix “plaquette” products is similarly invariant. In this paper,...