scholarly journals Lattices Generated by Two Orbits of Subspaces under Finite Singular Symplectic Groups

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Xuemei Liu
Keyword(s):  
Classical Group ◽  
Symplectic Space ◽  
Symplectic Groups ◽  
Characteristic Polynomials ◽  
Finite Classical Group

In the paper titled “Lattices generated by two orbits of subspaces under finite classical group” by Wang and Guo. The subspaces in the lattices are characterized and the geometricity is classified. In this paper, the result above is generalized to singular symplectic space. This paper characterizes the subspaces in these lattices, classifies their geometricity, and computes their characteristic polynomials.

On the Genus of a Finite Classical Group

1997 ◽  
Vol 29 (2) ◽  
pp. 159-164
Author(s):  
Martin W. Liebeck ◽  
Chris Wayman Purvis
Keyword(s):  
Classical Group ◽  
Finite Classical Group

The Steinberg Character of Finite Classical Groups

2013 ◽  
Vol 20 (01) ◽  
pp. 163-168
Author(s):  
Xueling Song ◽  
Yanjun Liu
Keyword(s):  
Classical Group ◽  
Classical Groups ◽  
Characteristic P ◽  
Combinatorial Objects ◽  
Finite Classical Group ◽  
Finite Classical Groups ◽  
Steinberg Character

Let G be a finite classical group of characteristic p. In this paper, we give an arithmetic criterion of the primes r ≠ p, for which the Steinberg character lies in the principal r-block of G. The arithmetic criterion is obtained from some combinatorial objects (the so-called partition and symbol).

MINIMAL IRREDUCIBILITY AND THE UNIPOTENT CHARACTERS OF GROUPS OF TYPE Bm AND Cm

2009 ◽  
Vol 08 (03) ◽  
pp. 413-451
Author(s):  
L. DI MARTINO ◽  
M. A. PELLEGRINI ◽  
TH. WEIGEL
Keyword(s):  
Classical Group ◽  
Proper Subgroup ◽  
Type B ◽  
Finite Classical Group

In this paper we prove that the (non-trivial) irreducible complex unipotent characters of a finite classical group G of type Bm or Cm in odd characteristic are reducible over any proper subgroup of G, apart from very few notable exceptions.

The probability of generating a finite classical group

1990 ◽  
Vol 36 (1) ◽  
Author(s):  
WilliamM. Kantor ◽  
Alexander Lubotzky
Keyword(s):  
Classical Group ◽  
Finite Classical Group

Prolonging Nerve Grafts Using Chemical Extracted Muscle-in-vein with Vein Window Method Chemical acellular nerve grafts

2018 ◽  
Vol 68 (12) ◽  
pp. 2936-2940
Author(s):  
Irina Mihaela Jemnoschi Hreniuc ◽  
Camelia Tamas ◽  
Sorin Aurelian Pasca ◽  
Bogdan Ciuntu ◽  
Roxana Ciuntu ◽  
...  
Keyword(s):  
Classical Group ◽  
Donor Site ◽  
Good Alternative ◽  
Nerve Graft ◽  
Male Rats ◽  
Chemical Extraction ◽  
Nerve Grafting ◽  
Nerve Grafts ◽  
Local Resources ◽  
Window Method

Nerve injuries are a common pathology in hand trauma. The consequences are drastic both for patients and doctors/medical system. In many cases direct coaptation is impossible. A nerve graft should be used in the case of a neuroma, trauma or tumor, for restoration of nervous influx. The aim of this study is demonstrate that by grafting restant nerve stumps with muscle-in-vein nerve grafts we obtain good result in terms of functional and sensibility recovery and also our method �window-vein� is a good way of prolonging nerve grafts. The method of study is experimental. We worked in the laboratory in optimal conditions for carrying out of muscles-in-vein nerve grafts (nerve grafts size 1.5 cm-3 cm). We used acellular muscle grafts with the chemical extraction method.The study was conducted on experimental animals (Wistar male rats).We used 30 experience animals in 3 equal groups (classical group and muscle-in-vein nerve grafts-2 nerve grafts of 1,5 cm central sutured and the third group with muscle-in-vein nerve grafts, window-vein method, 3 cm). At 4 and respectively 6 weeks postoperative at the quality tests we observed the progress with the footprint test. The operated hind in comparison with the healthy hind was 86% recovered and similar with classic nerve grafts. Quantitatively the number of regenerated axons in the group with muscle-in-vein nerve grafts was significant bigger in comparison with the classical group (15%).The method using muscle-in-vein nerve graft with windows-vein it�s a good alternative for nerve grafting in comparison with classical nerve grafting. When the local possibilities are limited, this method is good for prolonging the grafts. The relationship between cost and benefit in this case it�s an advantage because we use the local resources of the affected area. The motor results of nerve grafting ingroup 2 in comparison with group 3 were similar and in some cases better in group 1. Grafting with MVNG offers a better alternative for donor site regeneration in comparison with classical nerve grafts. This method is useful to prolong nerve grafts without adding morbidity.

scholarly journals R-GROUP AND WHITTAKER SPACE OF SOME GENUINE REPRESENTATIONS

2021 ◽  
pp. 1-61
Author(s):  
Fan Gao
Keyword(s):  
Series Representation ◽  
Principal Series ◽  
Symplectic Groups ◽  
Principal Series Representation ◽  
Connected Group ◽  
Covering Group ◽  
Simply Connected

Abstract 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 the Whittaker space for the irreducible constituents of such a principal series representation. Moreover, for certain saturated covers of a semisimple simply connected group, we also propose a simpler conjectural formula for such dimensions. This latter conjectural formula is verified in several cases, including covers of the symplectic groups.

-ADIC -FUNCTIONS FOR ORDINARY FAMILIES ON SYMPLECTIC GROUPS

2019 ◽  
Vol 19 (4) ◽  
pp. 1287-1347 ◽  
Author(s):  
Zheng Liu
Keyword(s):  
Eisenstein Series ◽  
Symplectic Group ◽  
Symplectic Groups ◽  
Simple Strategy ◽  
Doubling Method

We construct the $p$-adic standard $L$-functions for ordinary families of Hecke eigensystems of the symplectic group $\operatorname{Sp}(2n)_{/\mathbb{Q}}$ using the doubling method. We explain a clear and simple strategy of choosing the local sections for the Siegel Eisenstein series on the doubling group $\operatorname{Sp}(4n)_{/\mathbb{Q}}$, which guarantees the nonvanishing of local zeta integrals and allows us to $p$-adically interpolate the restrictions of the Siegel Eisenstein series to $\operatorname{Sp}(2n)_{/\mathbb{Q}}\times \operatorname{Sp}(2n)_{/\mathbb{Q}}$.

Bounds on subspace codes based on totally isotropic subspace in symplectic spaces and extended symplectic spaces

2019 ◽  
Vol 12 (05) ◽  
pp. 1950069
Author(s):  
Mahdieh Hakimi Poroch
Keyword(s):  
Sphere Packing ◽  
Symplectic Space ◽  
Isotropic Subspace ◽  
Subspace Codes ◽  
Singleton Bound ◽  
Symplectic Spaces ◽  
Isotropic Subspaces ◽  
Totally Isotropic Subspace ◽  
Totally Isotropic Subspaces

In this paper, we propose the Sphere-packing bound, Singleton bound and Gilbert–Varshamov bound on the subspace codes [Formula: see text] based on totally isotropic subspaces in symplectic space [Formula: see text] and on the subspace codes [Formula: see text] based on totally isotropic subspace in extended symplectic space [Formula: see text].

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