scholarly journals Representation theoretic realization of non-symmetric Macdonald polynomials at infinity

2020 ◽  
Vol 2020 (764) ◽  
pp. 181-216 ◽  
Author(s):  
Evgeny Feigin ◽  
Syu Kato ◽  
Ievgen Makedonskyi
Keyword(s):  
Macdonald Polynomials ◽  
Schubert Varieties ◽  
Dual Spaces ◽  
Points Of View ◽  
Demazure Modules

AbstractWe study the non-symmetric Macdonald polynomials specialized at infinity from various points of view. First, we define a family of modules of the Iwahori algebra whose characters are equal to the non-symmetric Macdonald polynomials specialized at infinity. Second, we show that these modules are isomorphic to the dual spaces of sections of certain sheaves on the semi-infinite Schubert varieties. Third, we prove that the global versions of these modules are homologically dual to the level one affine Demazure modules for simply-laced Dynkin types except for type {\mathrm{E}_{8}}.

scholarly journals Cyclic Demazure Modules and Positroid Varieties

10.37236/8383 ◽  
2019 ◽  
Vol 26 (2) ◽  
Author(s):  
Thomas Lam
Keyword(s):  
Canonical Basis ◽  
Schubert Varieties ◽  
Coordinate Ring ◽  
Demazure Module ◽  
Demazure Modules

A positroid variety is an intersection of cyclically rotated Grassmannian Schubert varieties.  Each graded piece of the homogeneous coordinate ring of a positroid variety is the intersection of cyclically rotated (rectangular) Demazure modules, which we call the cyclic Demazure module.  In this note, we show that the cyclic Demazure module has a canonical basis, and define the cyclic Demazure crystal.

scholarly journals Macdonald polynomials and level two Demazure modules for affine sln+1

2021 ◽  
Vol 575 ◽  
pp. 159-191
Author(s):  
Rekha Biswal ◽  
Vyjayanthi Chari ◽  
Peri Shereen ◽  
Jeffrey Wand
Keyword(s):  
Macdonald Polynomials ◽  
Demazure Modules

scholarly journals Beilinson–Drinfeld Schubert varieties and global Demazure modules

2021 ◽  
Vol 9 ◽  
Author(s):  
Ilya Dumanski ◽  
Evgeny Feigin ◽  
Michael Finkelberg
Keyword(s):  
Line Bundle ◽  
Lie Algebra ◽  
Schubert Varieties ◽  
Affine Grassmannians ◽  
Demazure Modules ◽  
Determinant Line Bundle

Abstract We compute the spaces of sections of powers of the determinant line bundle on the spherical Schubert subvarieties of the Beilinson–Drinfeld affine Grassmannians. The answer is given in terms of global Demazure modules over the current Lie algebra.

High Resolution Specimen Area Imaged Under Negligible Field Aberrations

1970 ◽  
Vol 28 ◽  
pp. 540-541 ◽  
Author(s):  
T. Yanaka ◽  
K. Shirota
Keyword(s):  
High Resolution ◽  
Field Distribution ◽  
Image Space ◽  
Beam Deflection ◽  
Objective Lens ◽  
Resolution Limit ◽  
Leakage Flux ◽  
Specimen Area ◽  
Points Of View ◽  
Aberration Theory

It is significant to note field aberrations (chromatic field aberration, coma, astigmatism and blurring due to curvature of field, defined by Glaser's aberration theory relative to the Blenden Freien System) of the objective lens in connection with the following three points of view; field aberrations increase as the resolution of the axial point improves by increasing the lens excitation (k2) and decreasing the half width value (d) of the axial lens field distribution; when one or all of the imaging lenses have axial imperfections such as beam deflection in image space by the asymmetrical magnetic leakage flux, the apparent axial point has field aberrations which prevent the theoretical resolution limit from being obtained.

Crystal structure images of large gold clusters and growing crystals by HRTEM

1984 ◽  
Vol 42 ◽  
pp. 428-429
Author(s):  
L.R. Wallenberg ◽  
J.-O. Bovin ◽  
G. Schmid
Keyword(s):  
Crystal Structure ◽  
Nucleation And Growth ◽  
Close Packing ◽  
Gold Clusters ◽  
Molecular Weight Determination ◽  
Growth Mechanisms ◽  
Starting Point ◽  
Different Types ◽  
Nucleation And Growth Mechanisms ◽  
Points Of View

Metallic clusters are interesting from various points of view, e.g. as a mean of spreading expensive catalysts on a support, or following heterogeneous and homogeneous catalytic events. It is also possible to study nucleation and growth mechanisms for crystals with the cluster as known starting point.Gold-clusters containing 55 atoms were manufactured by reducing (C6H5)3PAuCl with B2H6 in benzene. The chemical composition was found to be Au9.2[P(C6H5)3]2Cl. Molecular-weight determination by means of an ultracentrifuge gave the formula Au55[P(C6H5)3]Cl6 A model was proposed from Mössbauer spectra by Schmid et al. with cubic close-packing of the 55 gold atoms in a cubeoctahedron as shown in Fig 1. The cluster is almost completely isolated from the surroundings by the twelve triphenylphosphane groups situated in each corner, and the chlorine atoms on the centre of the 3x3 square surfaces. This gives four groups of gold atoms, depending on the different types of surrounding.

مشروعية نكاح المتعة عند الإمامية الإثنى عشرية وموقف المذاهب الإسلامية منها

2019 ◽  
Vol 7 (2) ◽  
Author(s):  
fithriah wardi
Keyword(s):  
Analytical Methods ◽  
Points Of View

Both fuqaha (Moslem jurists) of the Sunni and the Shi’ah are in agreement that Mut’ah marriage was permitted at the beginning of Islam, based on Al-quran verses and Rasulullah (pbuh) hadiths. However, they disagree as to the annulment and permissibility. The Shi’as considered Mut’ah marriage as permitted until the Day of Resurrection, meanwhile the Sunni viewed it as forbidden. The execution of Mut’ah marriage has always been singled out as one of the specific features of the Shi’ite doctrine in which denying it means denial of the religion. They also believe that woman who practised Mut’ah marriage will result in her sins being forgiven. According to the Shi’ites, Mut’ah marriage is one of the biggest reasons for someone to be granted heaven, and his status be elevated to the rank of the Holy Prophet PBUH. Hence, it can be said that practicing Mut’ah marriage is one of the most crucial issues among the Shi’ite community which is totally contradicted to the Sunni doctrine which believed it is unlawful marriage and equalized to Zina (adultery). There is no doubt that this is one of the most important topics that lead to the dispute between the two schools of thought. Using the descriptive and analytical methods, this study aims to elaborate the views on the issue from Shi’ite and Sunni points of view based on various proofs (adillah) and their argumentations in supporting the views.

An Immanent Criticism of Urban Design in Montevideo

2019 ◽  
Vol 2 (1) ◽  
Author(s):  
Washington MORALES
Keyword(s):  
Urban Design ◽  
Applied Ethics ◽  
Form Of Life ◽  
Political Reality ◽  
Applied Philosophy ◽  
Points Of View ◽  
Philosophical Frameworks

The debate about the so called “excluding design” has been a focus for applied philosophy for several years. The structure of this debate is constituted by deontological and consequentialist’s applied ethics and as well as agonistic democratic approaches. This paper asks for the applicability of these points of view to the particular socio-political reality of Montevideo. Examining this reality closer, I hold that we cannot comprehend the recent aestheticization of the excluding design there through these contemporary philosophical frameworks. As an alternative philosophical procedure, I analyze the aestheticization of excluding design in Montevideo from Rahel Jaeggi’s immanent criticism. I hold that this process of aestheticization implies an ideological regressive “form of life”. And I also argue that the Uruguayan democracy is affected by this ideological regression. Nevertheless, because this aestheticization is not an exclusive Uruguayan phenomenon, this paper intends to open one direction in applied philosophy of urban design.

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