Vanishing cycles and Cartan eigenvectors (Q1707596)

In the paper under review the authors using ideas from the singularity theory study eigenvalues of Cartan matrices and their \(q\)-deformations in Givental's sense. In particular the author obtain relations between eigenvalues of matrices of type \(L+L^t\) and \(-L^{-1}L^t\). This result is applied to obtain some information about eigenvectors of Cartan matrices in the case \(A\). Then the cases \(E_6\), \(E_8\) are investigated using their decompositions into Sebastian-Thom products of \(A\)-type Cartan matrices. Finally the eigenvalues of \(q\)-deformations of Cartan matrices are discussed.