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In this article, we develop a process to symmetrize the irreducible admissible representation of $GL_N(mathbb{Q}_p)$, as a consequence we obtain a more geometric understanding of the coefficient $m(mathbf{b}, mathbf{a})$ appearing in the decomposition of parabolic inductions, which allows us to prove a conjecture posed by Zelevinsky.
Let T_n be the maximal torus of diagonal matrices in GL_n, t_n be the Lie algebra of T_n and let N_n=N_{GL_n}(T_n) be the normalizer of T_n in GL_n. Consider then the quotient stacks [t_n/N_n] and [gl_n/GL_n] for the conjugation actions. In this pape
In this paper we give a simple description of DT-invariants of double quivers without potential as the multiplicity of the Steinberg character in some representation associated with the quiver. When the dimension vector is indivisible we use this des
We define and study representations of quantum toroidal $gl_n$ with natural bases labeled by plane partitions with various conditions. As an application, we give an explicit description of a family of highest weight representations of quantum affine $gl_n$ with generic level.
In arXiv:0810.2076 we presented a conjecture generalizing the Cauchy formula for Macdonald polynomials. This conjecture encodes the mixed Hodge polynomials of the representation varieties of Riemann surfaces with semi-simple conjugacy classes at the
We begin this paper by reviewing the Langlands correspondence for unipotent representations of the exceptional group of type $G_2$ over a $p$-adic field $F$ and present it in an explicit form. Then we compute all ABV-packets, as defined in [CFM+21] f