On the Geometry of Varieties of Invertiblesymmetric and Skew - Symmetric
نویسنده
چکیده
denote the algebraic varieties of n n invertible symmetric and skew-symmetric matrices over a eld F, respectively. We rst show how the homotopy type of Sym(n; R) and the homology groups of Sk(n; R) can be determined using an alternative method to Iwasawa decomposition. Then, using recent results of Dimca and Lehrer, the weight polynomials of Sym(n; C) and Sk(n; C) are calculated.
منابع مشابه
The (R,S)-symmetric and (R,S)-skew symmetric solutions of the pair of matrix equations A1XB1 = C1 and A2XB2 = C2
Let $Rin textbf{C}^{mtimes m}$ and $Sin textbf{C}^{ntimes n}$ be nontrivial involution matrices; i.e., $R=R^{-1}neq pm~I$ and $S=S^{-1}neq pm~I$. An $mtimes n$ complex matrix $A$ is said to be an $(R, S)$-symmetric ($(R, S)$-skew symmetric) matrix if $RAS =A$ ($ RAS =-A$). The $(R, S)$-symmetric and $(R, S)$-skew symmetric matrices have a number of special properties and widely used in eng...
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