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Search: All articles in the CMB digital archive with keyword symmetric function

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1. CMB 2008 (vol 51 pp. 584)

Purbhoo, Kevin; Willigenburg, Stephanie van
On Tensor Products of Polynomial Representations
We determine the necessary and sufficient combinatorial conditions for which the tensor product of two irreducible polynomial representations of $\GL(n,\mathbb{C})$ is isomorphic to another. As a consequence we discover families of Littlewood--Richardson coefficients that are non-zero, and a condition on Schur non-negativity.

Keywords:polynomial representation, symmetric function, Littlewood--Richardson coefficient, Schur non-negative
Categories:05E05, 05E10, 20C30

2. CMB 1999 (vol 42 pp. 478)

Pruss, Alexander R.
A Remark On the Moser-Aubin Inequality For Axially Symmetric Functions On the Sphere
Let $\scr S_r$ be the collection of all axially symmetric functions $f$ in the Sobolev space $H^1(\Sph^2)$ such that $\int_{\Sph^2} x_ie^{2f(\mathbf{x})} \, d\omega(\mathbf{x})$ vanishes for $i=1,2,3$. We prove that $$ \inf_{f\in \scr S_r} \frac12 \int_{\Sph^2} |\nabla f|^2 \, d\omega + 2\int_{\Sph^2} f \, d\omega- \log \int_{\Sph^2} e^{2f} \, d\omega > -\oo, $$ and that this infimum is attained. This complements recent work of Feldman, Froese, Ghoussoub and Gui on a conjecture of Chang and Yang concerning the Moser-Aubin inequality.

Keywords:Moser inequality, borderline Sobolev inequalities, axially symmetric functions
Categories:26D15, 58G30

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