All Questions

Let $(Q,V)$ be a quadratic space over an algebraically closed field $k$. Let $$ SO_Q(k):= \{ \sigma \in GL(V) : Q(\sigma v) = Q(v) \ \text{for all} \ v \in V \ \text{and} \det(\sigma) = 1 \}$$ Let $L \...

Can anyone either direct me to an relatively elementary proof in the literature--or show me why this (Conjecture 1 stated below) is true--or if I am mistaken and it is not true: For any 4-tuple $\xi =...

Let $F$ be a local field with valuation ring $R$. $V$ is a n dimensional non-singular quadratic space over $F$ with bilinear form $B$ and quadratic map $Q$. As usual, $O(V)$ denotes the orthogonal ...

Let $q$ be a rational quadratic form. How can we think of a Cartan decomposition of $O_q(Q_p)$? Is there a notion of Cartan involution for p-adic field, so that we can execute same process as we do ...