arXiv subjects
Publications and source records attributed to Sudip Mazumder.
Let $\F$ be a field with a non-trivial involution $c: α\to α^c$. An element $g \in {\rm GL}_n(\F)$ is called $c$-real if it is conjugate to $(g^c)^{-1}$. We prove that for $n \geq 2$, $g \in {\rm GL}_n(\F)$ is $c$-real if and only if it has a representation in some unitary group of degree $n$ over $\F$.
Let $\F$ be a field of characteristic different from $2$ and $\V$ be a vector space over $\F$. Let $J: α\to α^J$ be a fixed involutory automorphism on $\F$. In this paper we answer the following question: given an invertible linear map $T: \V \to \V$, when does the vector space $\V$ admit a $T$-invariant non-degenerate $J$-hermitian, resp. $J$-skew-hermitian, form?