On the singularity of the irreducible components of a Springer fiber in sl(n)

Let ${\mathcal B}_u$ be the Springer fiber over a nilpotent endomorphism $u\in End(\mathbb{C}^n)$. Let $J(u)$ be the Jordan form of $u$ regarded as a partition of $n$. The irreducible components of ${\mathcal B}_u$ are all of the same dimension. They are labelled by Young tableaux of shape $J(u)$. We study the question of singularity of the components of ${\mathcal B}_u$ and show that all the components of ${\mathcal B}_u$ are nonsingular if and only if $J(u)\in\{(\lambda,1,1,...), (\lambda_1,\lambda_2), (\lambda_1,\lambda_2,1), (2,2,2)\}$.Comment: 19 page

The states 1^1\Sigma^+_u, 1^1\Pi_u and 2^1\Sigma^+_u of Sr_2 studied by Fourier-transform spectroscopy

A high resolution study of the electronic states 1^1\Sigma^+_u and 1^1\Pi_u which belong to the asymptote 4^1D + 5^1S and of the state 2(A)^1\Sigma^+_u, which correlates to the asymptote 5^1P + 5^1S, is performed by Fourier-transform spectroscopy of fluorescence progressions induced by single frequency laser excitation. Precise descriptions of the potentials up to 2000 cm^{-1} above the bottom are derived and compared to currently available ab initio calculations. Especially for the state 1^1\Sigma^+_u large deviations are found. Rather weak and local perturbations are observed for the states 1^1\Pi_u and 2^1\Sigma^+_u, while a strong coupling of the state 1^1\Sigma^+_u to the component \Omega=0^+_u of the state 1^3\Pi_u, which belongs to the asymptote 5^3P + 5^1S, is indicated.Comment: Typing errors corrected (including numbers in table IX), 12 pages, 9 figure