A symmetric Bloch–Okounkov theorem

A Conjugacy Theorem for Symmetric Spaces

In this paper we prove that two Cartan subspaces of a semisimple symmetric pair (g, τ) are conjugate under G = Int(g) if and only if they are conjugate under (Gτ )0. Moreover we derive a double coset decomposition for G, which improves the results of Oshima and Matsuki.

A Lifting Theorem for Symmetric Commutants

Let T1, . . . , Tn ∈ B(H) be bounded operators on a Hilbert space H such that T1T ∗ 1 + · · · + TnT ∗ n ≤ IH. Given a symmetry j on H, i.e., j2 = j∗j = IH, we define the j-symmetric commutant of {T1, . . . , Tn} to be the operator space {A ∈ B(H) : TiA = jATi, i = 1, . . . , n}. In this paper we obtain lifting theorems for symmetric commutants. The result extends the Sz.-Nagy–Foiaş commutant li...

Symmetric Versions of Laman's Theorem

Recent work has shown that if an isostatic bar and joint framework possesses non-trivial symmetries, then it must satisfy some very simply stated restrictions on the number of joints and bars that are ‘fixed’ by various symmetry operations of the framework. For the group C3 which describes 3-fold rotational symmetry in the plane, we verify the conjecture proposed in [4] that these restrictions ...

Extension of the Douady-Hubbard's Theorem on Connectedness of the Mandelbrot Set to Symmetric Polynimials

Beurling’s Theorem for Riemannian Symmetric Spaces Ii

We prove two versions of Beurling’s theorem for Riemannian symmetric spaces of arbitrary rank. One of them uses the group Fourier transform and the other uses the Helgason Fourier transform. This is the master theorem in the quantitative uncertainty principle.