10 problems

Let $G$ be a reductive group over $F$, let $\rho$ be the representation defining the reductive monoid $X_\rho$, and let $C^(X_\rho(F))$ be the space of locally constant functions o…

Let $G$ be a reductive group over $F$, let $\rho$ define the reductive monoid $X_\rho$, and write $\mathcal{S}_{\mathrm{ES}}(X_\rho(F)):=C^\infty_c(X_\rho(F))$. View these function…

Let $G$ be a reductive group over $F$, let $\rho$ define the reductive monoid $X_\rho$, and let $C^\infty_c(X_\rho(F))$ be the space of compactly supported locally constant functio…

Let $N\in\mathbb{N}$, $a>0$, and let $\Delta_k$ denote the Dunkl Laplacian. Define $\mathcal{S}_{k,a}(\mathbb{R}^N)$ as the space of all functions…

Let $F$ be the field in the paper, let $P$ be the relevant parabolic subgroup, and let $X_P^{\circ}(F) \subset X_P(F)$ be the open subset appearing in the construction of the Schwa…

Isomorphism conjecture. In the Archimedean case, this push-forward map is an isomorphism.

For a locally convex space $X$ with the system $\mathscr U_0(X)$ of absolutely convex $0$-neighbourhoods, define its diametral dimension by … Define also … where $\mathscr B(X)$ is…

Let $P$ be a parabolic subgroup with Levi component $M$, let $X_P$ be the associated spherical variety, and set $\mathcal{S}:=\mathcal{S}(X_P)$. Let…

Let $M$ be the Levi component of a parabolic subgroup $P$, let $M_\mathrm{ab}$ be its abelianization, and let $\mathcal{S}(X_P)$ be the Schwartz space. Choose a Haar measure…

Let $G^\Box$ be the ambient reductive group, $P$ a parabolic subgroup with Levi component $M$, and $X_P=P_{\mathrm{der}}\backslash G^\Box$. Let $\overline{X_P}^\text{aff}$ be the a…