This paper develops precise asymptotic formulas for expanding non-spherical averages on compact quotients of real rank-one Lie groups, focusing on $SO(n,1)$ as a model case. Using tools from...

We prove that the center of the affine Lie algebra $\widehat{\mathfrak{gl}}_{n|1}$ at the critical level is generated by the coefficients in the expansion of the pseudo-differential operator...

The aim of this short research note is to present some results about a conjecture of Barker and Gelvin claiming that any source algebra of a block of a finite group has the unit group containing a...

Over the past three decades, there have been several attempts to characterize modules over affine Lie superalgebras. One of the main issues in this regard is dealing with zero-level modules. In...

The log-concavity of cluster variables of type $A_n$ and cluster monomials of type $A_2$ was established by Chen-Huang-Sun. It is still a conjecture for the cluster monomials of higher rank. In...

We study simple $\mathfrak{sl}(2)$-modules over $\mathbb C$ that are free of finite rank as $U(\mathfrak h)$-modules, where $\mathfrak h$ is a Cartan subalgebra of $\mathfrak{sl}(2)$. Our main...

In this article, we deeply investigate some properties of fuzzy negations induced from fuzzy conjunctions (resp. disjunctions), which are then applied to characterizing the fuzzy negations. We...

We introduce the notion of geometric purity in rigidly-compactly generated tt-categories by considering exact triangles that are pure at each tt-stalk. We develop a systematic study of this...

We study some homological properties of the parabolic induction functor for the $p$-adic general linear group. We obtain an embedding theorem of Ext-groups in the context of parabolic induction....

Let G be a possibly disconnected reductive real Lie group. In this paper, I parametrize the set of irreductible tempered characters of G. I then describe these characters using certain...

We study degenerate principal series representations of the split real group $G_{2(2)}$ induced from a character of a maximal parabolic subgroup whose unipotent radical is a Heisenberg group....

We study tropicalisations of quasi-automorphisms of cluster algebras and show that their induced action on the g-vectors can be realized by tropicalising their action on the homogeneous $\hat{y}$...

We propose a framework of monoidal categorification of finite type cluster algebras involving triangulated monoidal categories. Namely, given a Dynkin quiver $Q$, we consider the bounded homotopy...

Let $θ$ be an involution of a complex semisimple Lie algebra $\mathfrak{g}$ and $(\mathrm{U}_v,\mathrm{U}^\imath_v)$ be the associated quantum symmetric pair at an odd root of unity $v$. In...

For a permutation $z$ in the symmetric group $\mathrm{S}_{n}$, denote by $L_{z}$ the corresponding simple highest weight module in the principal block of the BGG category $\mathcal{O}$ for the Lie...

Let $ρ: Γ\longrightarrow G$ be a Zariski dense irreducible convex representation of the hyperbolic group $Γ$, where G is a connected real semisimple algebraic Lie group. We...

In this short note we show that every connected reductive simply-connected algebraic group of rank $>1$ over the complex numbers has infinitely many pairs of irreducible representations which are...