On the unramified Eisenstein spectrum
D Kazhdan, A Okounkov - arXiv preprint arXiv:2203.03486, 2022 - arxiv.org
For a split reductive group ${}^ LG $ over a global field, we determine the spectrum of the
spherical Hecke algebra coming from the unramified Eisenstein series for the minimal …
spherical Hecke algebra coming from the unramified Eisenstein series for the minimal …
Residue distributions, iterated residues, and the spherical automorphic spectrum
M De Martino, V Heiermann, E Opdam - arXiv preprint arXiv:2207.06773, 2022 - arxiv.org
Let $ G $ be a split reductive group over a number field $ F $. We consider the computation
of the inner product of two $ K $-spherical pseudo Eisenstein series of $ G $ supported in …
of the inner product of two $ K $-spherical pseudo Eisenstein series of $ G $ supported in …
L-function genera and applications
D Kazhdan, A Okounkov - arXiv preprint arXiv:2311.17747, 2023 - arxiv.org
We introduce equivariant L-genera associated to actions of Galois and related groups on
algebraic varieties. We explain the role which these L-genera play in the spectral analysis of …
algebraic varieties. We explain the role which these L-genera play in the spectral analysis of …
The generalized injectivity conjecture
S Dijols - arXiv preprint arXiv:1904.02525, 2019 - arxiv.org
We prove a conjecture of Casselman and Shahidi stating that the unique irreducible generic
subquotient of a standard module is necessarily a subrepresentation for a large class of …
subquotient of a standard module is necessarily a subrepresentation for a large class of …
[PDF][PDF] Some perspectives on Eisenstein series
E Lapid - arXiv preprint arXiv:2204.02914, 2022 - arxiv.org
arXiv:2204.02914v1 [math.NT] 6 Apr 2022 Page 1 arXiv:2204.02914v1 [math.NT] 6 Apr 2022
SOME PERSPECTIVES ON EISENSTEIN SERIES EREZ LAPID Abstract. We review some …
SOME PERSPECTIVES ON EISENSTEIN SERIES EREZ LAPID Abstract. We review some …
On Arthur's unitarity conjecture for split real groups
J Hundley, SD Miller - American Journal of Mathematics, 2022 - muse.jhu.edu
Arthur's conjectures predict the existence of some very interesting unitary representations
occurring in spaces of automorphic forms. We prove the unitarity of the``Langlands …
occurring in spaces of automorphic forms. We prove the unitarity of the``Langlands …
Supersymmetric Yang--Mills Matrix Integrals Revisited
R Eager - arXiv preprint arXiv:1909.13798, 2019 - arxiv.org
We evaluate the twisted partition function of four-dimensional $\mathcal {N}= 1$
supersymmetric Yang--Mills theory reduced to a point for all simple gauge groups. The …
supersymmetric Yang--Mills theory reduced to a point for all simple gauge groups. The …
[PDF][PDF] The residual spectrum of ; contribution from Borel subgroups
HH Kim - Bulletin of the Iranian Mathematical Society, 2017 - bims.iranjournals.ir
In this paper we study the residual spectrum of the quasi-split unitary group $ G= U (n, n) $
defined over a number field $ F $, coming from the Borel subgroups, $ L_ {dis}^ 2 (G …
defined over a number field $ F $, coming from the Borel subgroups, $ L_ {dis}^ 2 (G …