scholarly journals Limits under conjugacy of the diagonal subgroup in $SL_n(\mathbb {R})$

2015 ◽  
Vol 144 (8) ◽  
pp. 3243-3254 ◽  
Author(s):  
Arielle Leitner
Keyword(s):  
Diagonal Subgroup

scholarly journals On Pairs of Additive Subgroups Associated with Intermediate Subgroups of Groups of Lie Type over Nonperfect Fields

2021 ◽  
Vol 14 (5) ◽  
pp. 604-610
Author(s):  
Yakov N. Nuzhin ◽  
Keyword(s):  
Algebraic Extension ◽  
Chevalley Groups ◽  
Intermediate Subgroups ◽  
Diagonal Subgroup ◽  
Groups Of Lie Type ◽  
Nonperfect Field

The author has previously (Trudy IMM UrO RAN, 19(2013), no. 3) described the groups lying between twisted Chevalley groups G(K) and G(F) of type 2Al, 2Dl, 2E6, 3D4 in the case when the larger field F is an algebraic extension of the smaller nonperfect field K of exceptional characteristic for the group G(F) (characteristics 2 and 3 for the type 3D4 and only 2 for other types). It turned out that apart from, perhaps, the type 2Dl, such intermediate subgroups are standard, that is, they are exhausted by the groups G(P)H for some intermediate subfield P, K ⊆ P ⊆ F, and of the diagonal subgroup H normalizing the group G(P). In this note, it is established that intermediate subgroups are also standard for the type 2Dl

scholarly journals Equidistribution of joinings under off-diagonal polynomial flows of nilpotent Lie groups

2012 ◽  
Vol 33 (6) ◽  
pp. 1667-1708 ◽  
Author(s):  
TIM AUSTIN
Keyword(s):  
Lie Group ◽  
Nilpotent Lie Groups ◽  
Nilpotent Lie Group ◽  
Norm Convergence ◽  
Ergodic Averages ◽  
Multiple Recurrence ◽  
Polynomial Maps ◽  
Image Position ◽  
Polynomial Flows ◽  
Diagonal Subgroup

AbstractLet $G$ be a connected nilpotent Lie group. Given probability-preserving$G$-actions $(X_i,\Sigma _i,\mu _i,u_i)$, $i=0,1,\ldots ,k$, and also polynomial maps $\phi _i:\mathbb {R}\to G$, $i=1,\ldots ,k$, we consider the trajectory of a joining $\lambda $ of the systems $(X_i,\Sigma _i,\mu _i,u_i)$ under the ‘off-diagonal’ flow \[ (t,(x_0,x_1,x_2,\ldots ,x_k))\mapsto (x_0,u_1^{\phi _1(t)}x_1,u_2^{\phi _2(t)}x_2,\ldots ,u_k^{\phi _k(t)}x_k). \] It is proved that any joining $\lambda $ is equidistributed under this flow with respect to some limit joining $\lambda '$. This is deduced from the stronger fact of norm convergence for a system of multiple ergodic averages, related to those arising in Furstenberg’s approach to the study of multiple recurrence. It is also shown that the limit joining $\lambda '$ is invariant under the subgroup of $G^{k+1}$generated by the image of the off-diagonal flow, in addition to the diagonal subgroup.

How does Diagonal Subgroup Embedding Determine the Structure of a Group?

2016 ◽  
Vol 4 (4) ◽  
pp. 423-433
Author(s):  
Shouhong Qiao ◽  
Guohua Qian ◽  
Yanming Wang
Keyword(s):  
Diagonal Subgroup

scholarly journals Periods of automorphic forms: the case of

2014 ◽  
Vol 151 (4) ◽  
pp. 665-712 ◽  
Author(s):  
Atsushi Ichino ◽  
Shunsuke Yamana
Keyword(s):  
Automorphic Form ◽  
Automorphic Forms ◽  
Selberg Integral ◽  
Selberg Integrals ◽  
Diagonal Subgroup ◽  
Periods Of Automorphic Forms

Following Jacquet, Lapid and Rogawski, we define a regularized period of an automorphic form on $\text{GL}_{n+1}\times \text{GL}_{n}$ along the diagonal subgroup $\text{GL}_{n}$ and express it in terms of the Rankin–Selberg integral of Jacquet, Piatetski-Shapiro and Shalika. This extends the theory of Rankin–Selberg integrals to all automorphic forms on $\text{GL}_{n+1}\times \text{GL}_{n}$.

scholarly journals A nonhomogeneous orbit closure of a diagonal subgroup

2010 ◽  
Vol 171 (1) ◽  
pp. 557-570 ◽  
Author(s):  
François Maucourant
Keyword(s):  
Orbit Closure ◽  
Diagonal Subgroup

On the Restriction to 𝒟* × 𝒟* of Representations of p-adic GL2(𝒟)

2007 ◽  
Vol 59 (5) ◽  
pp. 1050-1068 ◽  
Author(s):  
A. Raghuram
Keyword(s):  
Irreducible Representation ◽  
Division Algebra ◽  
Local Field ◽  
Joint Work ◽  
Invariant Distributions ◽  
Multiplicity One ◽  
Kirillov Theory ◽  
Multiplicity Free ◽  
Diagonal Subgroup ◽  
Quaternion Division Algebra

AbstractLet be a division algebra over a nonarchimedean local field. Given an irreducible representation π of GL2(), we describe its restriction to the diagonal subgroup × . The description is in terms of the structure of the twisted Jacquet module of the representation π. The proof involves Kirillov theory that we have developed earlier in joint work with Dipendra Prasad. The main result on restriction also shows that π is × -distinguished if and only if π admits a Shalika model. We further prove that if is a quaternion division algebra then the twisted Jacquetmodule is multiplicity-free by proving an appropriate theorem on invariant distributions; this then proves a multiplicity-one theorem on the restriction to × in the quaternionic case.

scholarly journals CONSTRUCTIVE WALL-CROSSING AND SEIBERG–WITTEN

2013 ◽  
Vol 28 (03n04) ◽  
pp. 1340005
Author(s):  
PILJIN YI
Keyword(s):  
Bound State ◽  
Low Energy ◽  
Marginal Stability ◽  
Energy Dynamics ◽  
Principle Solution ◽  
Wall Crossing ◽  
Rational Invariant ◽  
Equivariant Version ◽  
Bps States ◽  
Diagonal Subgroup

We outline a comprehensive and first-principle solution to the wall-crossing problem in D = 4N = 2 Seiberg–Witten theories. We start with a brief review of the multi-centered nature of the typical BPS states and of how this allows them to disappear abruptly as parameters or vacuum moduli are continuously changed. This means that the wall-crossing problem is really a bound state formation/dissociation problem. A low energy dynamics for arbitrary collections of dyons is derived, with the proximity to the so-called marginal stability wall playing the role of the small expansion parameter. We discover that the low energy dynamics of such BPS dyons cannot be reduced to one on the classical moduli space, [Formula: see text], yet the index can be phrased in terms of [Formula: see text]. The so-called rational invariant, first seen in Kontsevich–Soibelman formalism of wall-crossing, is shown to incorporate Bose/Fermi statistics automatically. Furthermore, an equivariant version of the index is shown to compute the protected spin character of the underlying D = 4N = 2 theory, where [Formula: see text] isometry of [Formula: see text] is identified as a diagonal subgroup of rotation SU(2)L and R-symmetry SU(2)R.

Sign in / Sign up

Export Citation Format

Share Document