26 citations · 52 across the 20 of their papers we have counts for
21 papers
Wavefront sets for genuine representations of -covers of Kazhdan--Patterson or Savin types
Fan Gao, Runze Wang, Jiandi Zou
First, we consider general Brylinski--Deligne covers of the -adic general linear groups, and discuss the theory of Bernstein--Zelevinsky derivatives. We also recall the Zelevins…
Geometric wavefront sets of genuine Iwahori-spherical representations
Fan Gao, Runze Wang
For Iwahori-spherical genuine representations of central covers with positive real Satake parameters, we prove the upper bound inequality for their geometric wavefront sets, formul…
Covering Barbasch-Vogan duality and wavefront sets of genuine representations
Fan Gao, Baiying Liu, Chi-Heng Lo +1
In this paper, we start by defining a covering Barbasch-Vogan duality and prove some of its properties. Then, for genuine representations of -adic covering groups we formulate a…
Gelfand-Kirillov dimensions and annihilator varieties of highest weight modules of exceptional Lie algebras
Zhanqiang Bai, Fan Gao, Yutong Wang +1
Let be an irreducible highest weight module of a complex simple Lie algebra of exceptional type, with highest weight , where is half the sum of positive roots. Its…
Quasi-admissible, raisable nilpotent orbits, and theta representations
Fan Gao, Baiying Liu, Wan-Yu Tsai
We study the quasi-admissibility and raisablility of some nilpotent orbits of a covering group. In particular, we determine the degree of the cover such that a given split nilpoten…
Formal degrees of genuine Iwahori-spherical representations
Ping Dong, Fan Gao, Runze Wang
For square-integrable genuine Iwahori-spherical representations of central covers, we verify the Hiraga--Ichino--Ikeda formula for their formal degrees. We also compute the Whittak…
Gelfand--Graev functor and quantum affine Schur--Weyl duality
Fan Gao, Nadya Gurevich, Edmund Karasiewicz
We explicate relations among the Gelfand--Graev modules for central covers, the Euler--Poincaré polynomial of the Arnold--Brieskorn manifold, and the quantum affine Schur--Weyl dua…
An effective and efficient algorithm for the Wigner rotation matrix at high angular momenta
Bin-Lei Wang, Fan Gao, Long-Jun Wang +1
The Wigner rotation matrix (-function), which appears as a part of the angular-momentum-projection operator, plays a crucial role in modern nuclear-structure models. However, it…
Genuine pro- Iwahori--Hecke algebras, Gelfand--Graev representations, and some applications
Fan Gao, Nadya Gurevich, Edmund Karasiewicz
We study the Iwahori-component of the Gelfand-Graev representation of a central cover of a split linear reductive group and utilize our results for three applications. In fact, it…
Restrictions, L-parameters, and local coefficients for genuine representations
Fan Gao, Freydoon Shahidi, Dani Szpruch
We consider the restriction and induction of representations between a covering group and its derived subgroup, both on the representation-theoretic side and the L-parameter side.…
On the wavefront sets associated with theta representations
Fan Gao, Wan-Yu Tsai
We study a conjectural formula for the maximal elements in the wavefront set associated with a theta representation of a covering group over -adic fields. In particular, it is s…
R-group and Whittaker space of some genuine representations
Fan Gao
For a unitary unramified genuine principal series representation of a covering group, we study the associated R-group. We prove a formula relating the R-group to the dimension of t…
Kazhdan-Lusztig representations and Whittaker space of some genuine representations
Fan Gao
We prove a formula for the dimension of Whittaker functionals of irreducible constituents of a regular unramified genuine principal series for covering groups. The formula explicit…
Local coefficients and gamma factors for principal series of covering groups
Fan Gao, Freydoon Shahidi, Dani Szpruch
We consider an -fold Brylinski-Deligne cover of a reductive group over a -adic field. Since the space of Whittaker functionals of an irreducible genuine representation of suc…
L-groups and the Langlands program for covering groups: a historical introduction
Wee Teck Gan, Fan Gao, Martin H. Weissman
In this joint introduction to an Asterisque volume, we give a short discussion of the historical developments in the study of nonlinear covering groups, touching on their structure…
Whittaker models for depth zero representations of covering groups
Fan Gao, Martin H. Weissman
We study the dimension of the space of Whittaker functionals for depth zero representations of covering groups. In particular, we determine such dimensions for arbitrary Brylinski-…
Generalized Bump-Hoffstein conjecture for coverings of the general linear groups
Fan Gao
In this paper, we investigate the extent to which the Bump-Hoffstein conjecture could be generalized for central coverings of general linear groups. We provide evidence for such ge…
Distinguished theta representations for certain covering groups
Fan Gao
For Brylinski-Deligne covering groups of an arbitrary split reductive group, we consider theta representations attached to certain exceptional genuine characters. The goal of the p…
The Gindikin-Karpelevich Formula and Constant Terms of Eisenstein Series for Brylinski-Deligne Extensions
Fan Gao
We firstly discuss properties of the L-group for Brylinski-Deligne (BD) extensions constructed by M. Weissman. Secondly, the Gindikin-Karpelevich (GK) formula for arbitrary BD exte…
The Langlands-Weissman Program for Brylinski-Deligne extensions
Wee Teck Gan, Fan Gao
We describe an evolving and conjectural extension of the Langlands program for a class of nonlinear covering groups of algebraic origin studied by Brylinski-Deligne. In particular,…
The Residual Spectrum of Mp_4(A_k)
Fan Gao
We compute the residual spectrum of the global metaplectic group Mp_4(A_k), by using the theory of Eisenstein series. The residual spectra obtained are interpreted as near equivale…