Toward Berenstein-Zelevinsky data in affine type 𝐴, Part II: Explicit description

2012 ◽  
pp. 185-216 ◽  
Author(s):  
Satoshi Naito ◽  
Daisuke Sagaki ◽  
Yoshihisa Saito
Keyword(s):  
Explicit Description ◽  
Affine Type

scholarly journals Mirković–Vilonen polytopes and Khovanov–Lauda–Rouquier algebras

2016 ◽  
Vol 152 (8) ◽  
pp. 1648-1696 ◽  
Author(s):  
Peter Tingley ◽  
Ben Webster
Keyword(s):  
Lie Algebras ◽  
Finite Type ◽  
General Type ◽  
The Other ◽  
Explicit Description ◽  
Affine Grassmannian ◽  
Combinatorial Description ◽  
Extra Information ◽  
Klr Algebras ◽  
Affine Type

We describe how Mirković–Vilonen (MV) polytopes arise naturally from the categorification of Lie algebras using Khovanov–Lauda–Rouquier (KLR) algebras. This gives an explicit description of the unique crystal isomorphism between simple representations of KLR algebras and MV polytopes. MV polytopes, as defined from the geometry of the affine Grassmannian, only make sense in finite type. Our construction on the other hand gives a map from the infinity crystal to polytopes for all symmetrizable Kac–Moody algebras. However, to make the map injective and have well-defined crystal operators on the image, we must in general decorate the polytopes with some extra information. We suggest that the resulting ‘KLR polytopes’ are the general-type analogues of MV polytopes. We give a combinatorial description of the resulting decorated polytopes in all affine cases, and show that this recovers the affine MV polytopes recently defined by Baumann, Kamnitzer, and the first author in symmetric affine types. We also briefly discuss the situation beyond affine type.

The Movement of Ezekiel’s “Living Beings” in 4Q405 Shirot ‘Olat Hashabbat. Part II: The Twelfth Song

Journal for Semitics ◽  
2018 ◽  
Vol 27 (1) ◽  
Author(s):  
Annette Evans
Keyword(s):  
Explicit Description ◽  
Plural Form ◽  
The Law ◽  
Mount Sinai

In this article descriptions of angelic movement in the Twelfth Song are compared to descriptions of such activity arising from the throne of God in Ezekiel’s vision in Ezekiel 1 and 10, and to that in the Seventh Song as contained in scroll 4Q403. The penultimate Twelfth Song of the Songs of the Sabbath Sacrifice culminates in a more explicit description of angelic messenger activity and in other nuances. The Twelfth Song was intended to be read on the Sabbath immediately following Shavu’ot, when the traditional synagogue reading is Ezekiel 1 and Exodus 19–20. The possible significance for the author of Songs of the Sabbath Sacrifice of the connection between the giving of the Law at Mount Sinai and Ezekiel’s vision where merkebah thrones and seats appear in the plural form is considered in the conclusion

scholarly journals Polynomial identities related to special Schubert varieties

2021 ◽  
Author(s):  
Francesca Cioffi ◽  
Davide Franco ◽  
Carmine Sessa
Keyword(s):  
Arbitrary Number ◽  
Schubert Variety ◽  
Decomposition Theorem ◽  
Point Of View ◽  
Explicit Description ◽  
Intersection Cohomology ◽  
Schubert Varieties ◽  
Polynomial Identities ◽  
PoincarĂŠ Polynomial

AbstractLet $$\mathcal S$$ S be a single condition Schubert variety with an arbitrary number of strata. Recently, an explicit description of the summands involved in the decomposition theorem applied to such a variety has been obtained in a paper of the second author. Starting from this result, we provide an explicit description of the PoincarĂŠ polynomial of the intersection cohomology of $$\mathcal S$$ S by means of the PoincarĂŠ polynomials of its strata, obtaining interesting polynomial identities relating PoincarĂŠ polynomials of several Grassmannians, both by a local and by a global point of view. We also present a symbolic study of a particular case of these identities.

scholarly journals Erythrocyte Membrane Model with Explicit Description of the Lipid Bilayer and the Spectrin Network

Biophysical Journal ◽  
2014 ◽  
Vol 107 (3) ◽  
pp. 642-653 ◽  
Author(s):  
He Li ◽  
George Lykotrafitis
Keyword(s):  
Lipid Bilayer ◽  
Erythrocyte Membrane ◽  
Explicit Description ◽  
Membrane Model ◽  
Spectrin Network

An Explicit Description of the Reproducing Kernel Hilbert Spaces of Gaussian RBF Kernels

2006 ◽  
Vol 52 (10) ◽  
pp. 4635-4643 ◽  
Author(s):  
I. Steinwart ◽  
D. Hush ◽  
C. Scovel
Keyword(s):  
Hilbert Spaces ◽  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Spaces ◽  
Explicit Description ◽  
Kernel Hilbert Spaces

Stability conditions and braid group actions on affine An quivers

2021 ◽  
pp. 2250174
Author(s):  
Chien-Hsun Wang
Keyword(s):  
Moduli Space ◽  
Braid Group ◽  
Group Actions ◽  
Stability Conditions ◽  
Quadratic Differentials ◽  
Spherical Subgroup ◽  
Type Formula ◽  
Affine Type

We study stability conditions on the Calabi–Yau-[Formula: see text] categories associated to an affine type [Formula: see text] quiver which can be constructed from certain meromorphic quadratic differentials with zeroes of order [Formula: see text]. We follow Ikeda’s work to show that this moduli space of quadratic differentials is isomorphic to the space of stability conditions quotient by the spherical subgroup of the autoequivalence group. We show that the spherical subgroup is isomorphic to the braid group of affine type [Formula: see text] based on the Khovanov–Seidel–Thomas method.

The Finite-dimensional Modular Lie Superalgebra Γ

Algebra Colloquium ◽  
2010 ◽  
Vol 17 (03) ◽  
pp. 525-540 ◽  
Author(s):  
Xiaoning Xu ◽  
Yongzheng Zhang ◽  
Liangyun Chen
Keyword(s):  
Lie Superalgebra ◽  
Lie Superalgebras ◽  
Explicit Description ◽  
Cartan Type ◽  
Modular Lie Superalgebra ◽  
New Family ◽  
Finite Dimensional ◽  
Derivation Superalgebra ◽  
Modular Lie Superalgebras

A new family of finite-dimensional modular Lie superalgebras Γ is defined. The simplicity and generators of Γ are studied and an explicit description of the derivation superalgebra of Γ is given. Moreover, it is proved that Γ is not isomorphic to any known Lie superalgebra of Cartan type.

scholarly journals Tensorial Square of the Hyperoctahedral Group Coinvariant Space

10.37236/1064 ◽  
2006 ◽  
Vol 13 (1) ◽  
Author(s):  
François Bergeron ◽  
Riccardo Biagioli
Keyword(s):  
Irreducible Representation ◽  
Explicit Description ◽  
Hyperoctahedral Group ◽  
Tensor Square

The purpose of this paper is to give an explicit description of the trivial and alternating components of the irreducible representation decomposition of the bigraded module obtained as the tensor square of the coinvariant space for hyperoctahedral groups.

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