scholarly journals Semi-infinite Plücker Relations and Weyl Modules

2018 ◽  
Vol 2020 (14) ◽  
pp. 4357-4394 ◽  
Author(s):  
Evgeny Feigin ◽  
Ievgen Makedonskyi
Keyword(s):  
Type A ◽  
Character Formula ◽  
Flag Varieties ◽  
Coordinate Ring ◽  
Weyl Modules ◽  
Plücker Relations ◽  
Plücker Embedding ◽  
Formal Version ◽  
The Ideal

Abstract The goal of this paper is two-fold. First, we write down the semi-infinite Plücker relations, describing the Drinfeld–Plücker embedding of the (formal version of) semi-infinite flag varieties in type A. Second, we study the homogeneous coordinate ring, that is, the quotient by the ideal generated by the semi-infinite Plücker relations. We establish the isomorphism with the algebra of dual global Weyl modules and derive a new character formula.

The short-term prognostic value of serum platelet to hemoglobin in patients with type A acute aortic dissection

Perfusion ◽  
2020 ◽  
pp. 026765912098222
Author(s):  
Yu Wang ◽  
Tengfei Qiao ◽  
Jun Zhou
Keyword(s):  
Aortic Dissection ◽  
Hospital Mortality ◽  
Acute Aortic Dissection ◽  
Independent Predictor ◽  
Type A ◽  
Short Term ◽  
Survivor Group ◽  
Mortality Hazard ◽  
Mortality Hazard Ratio ◽  
The Ideal

Purpose: Type A acute aortic dissection (AAD) is an uncommon catastrophic cardiovascular disease with high pre-hospital mortality rate without timely and effectively treated. The aim of this study was to assess the value of serum platelet to hemoglobin (PHR) in predicting in-hospital mortality in type A AAD patients. Methods: A total of 183 type A AAD patients were included in this retrospective investigation from January 2017 to December 2019. Admission blood routine parameters were gathered and PHR was computed. The outcome was all-cause in-hospital mortality within 30 days. Results The average levels of serum PHR were significant higher in survivor group than those in non-survivor group (1.14 ± 0.57 vs 0.87 ± 0.47, p = 0.006) and serum PHR was an independent factor associated with in-hospital mortality (hazard ratio (HR): 2.831; 95% confidence interval (CI): 1.108–7.231; p = 0.030). ROC noted that 0.8723 was chosen as the ideal cutoff value with a sensitivity of 64.3% and specificity of 72.5%. In addition, the area under the ROC curve (AUC) was 0.693 (95% CI 0.599–0.787, p < 0.001). Conclusion: Admission serum PHR can be used as an independent predictor of in-hospital mortality in patients with type A AAD.

scholarly journals Toward AGT for Parabolic Sheaves

2020 ◽  
Author(s):  
Andrei Neguţ
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Conformal Field Theory ◽  
Moduli Spaces ◽  
Type A ◽  
Conformal Field ◽  
Toroidal Algebra ◽  
Agt Correspondence ◽  
K Theory ◽  
The Ideal

Abstract We construct explicit elements $W_{ij}^k$ in (a completion of) the shifted quantum toroidal algebra of type $A$ and show that these elements act by 0 on the $K$-theory of moduli spaces of parabolic sheaves. We expect that the quotient of the shifted quantum toroidal algebra by the ideal generated by the elements $W_{ij}^k$ will be related to $q$-deformed $W$-algebras of type $A$ for arbitrary nilpotent, which would imply a $q$-deformed version of the Alday-Gaiotto-Tachikawa (AGT) correspondence between gauge theory with surface operators and conformal field theory.

scholarly journals K-Theoretic J-Functions of Type A Flag Varieties

2012 ◽  
Vol 2013 (16) ◽  
pp. 3647-3677
Author(s):  
K. Taipale
Keyword(s):  
Type A ◽  
Flag Varieties

scholarly journals THE COMBINATORICS OF TENSOR PRODUCTS OF HIGHER AUSLANDER ALGEBRAS OF TYPE A

2020 ◽  
pp. 1-21
Author(s):  
JORDAN MCMAHON ◽  
NICHOLAS J. WILLIAMS
Keyword(s):  
Tensor Product ◽  
Tensor Products ◽  
Type A ◽  
Coordinate Ring ◽  
Preprojective Algebra ◽  
Finite Algebras ◽  
Plücker Coordinates ◽  
Higher Dimensional ◽  
Dimensional Version

Abstract We consider maximal non-l-intertwining collections, which are a higher-dimensional version of the maximal non-crossing collections which give clusters of Plücker coordinates in the Grassmannian coordinate ring, as described by Scott. We extend a method of Scott for producing such collections, which are related to tensor products of higher Auslander algebras of type A. We show that a higher preprojective algebra of the tensor product of two d-representation-finite algebras has a d-precluster-tilting subcategory. Finally, we relate mutations of these collections to a form of tilting for these algebras.

scholarly journals Chevalley-Monk and Giambelli formulas for Peterson Varieties

2014 ◽  
Vol DMTCS Proceedings vol. AT,... (Proceedings) ◽  
Author(s):  
Elizabeth Drellich
Keyword(s):  
Cohomology Ring ◽  
Quantum Cohomology ◽  
Type A ◽  
Flag Variety ◽  
Flag Varieties ◽  
Dimensional Torus ◽  
One Dimensional ◽  
International Audience ◽  
Schubert Classes ◽  
Partial Flag Varieties

International audience A Peterson variety is a subvariety of the flag variety $G/B$ defined by certain linear conditions. Peterson varieties appear in the construction of the quantum cohomology of partial flag varieties and in applications to the Toda flows. Each Peterson variety has a one-dimensional torus $S^1$ acting on it. We give a basis of Peterson Schubert classes for $H_{S^1}^*(Pet)$ and identify the ring generators. In type A Harada-Tymoczko gave a positive Monk formula, and Bayegan-Harada gave Giambelli's formula for multiplication in the cohomology ring. This paper gives a Chevalley-Monk rule and Giambelli's formula for all Lie types.

scholarly journals Flag Gromov-Witten invariants via crystals

2014 ◽  
Vol DMTCS Proceedings vol. AT,... (Proceedings) ◽  
Author(s):  
Jennifer Morse ◽  
Anne Schilling
Keyword(s):  
Weyl Group ◽  
Type A ◽  
Schubert Calculus ◽  
Schur Function ◽  
Flag Varieties ◽  
Highest Weight ◽  
Affine Weyl Group ◽  
Nous Montrons ◽  
International Audience ◽  
Complete Flag

International audience We apply ideas from crystal theory to affine Schubert calculus and flag Gromov-Witten invariants. By defining operators on certain decompositions of elements in the type-$A$ affine Weyl group, we produce a crystal reflecting the internal structure of Specht modules associated to permutation diagrams. We show how this crystal framework can be applied to study the product of a Schur function with a $k$-Schur function. Consequently, we prove that a subclass of 3-point Gromov-Witten invariants of complete flag varieties for $\mathbb{C}^n$ enumerate the highest weight elements under these operators. Nous appliquons des idées provenant de la théorie des bases cristallines au calcul de Schubert affine et aux invariants de drapeaux de Gromov–Witten. Nous définissons des opérateurs sur certaines décompositions d’éléments de groupes de Weyl affines en type $A$ afin de construire une base cristalline encodant la structure interne des modules de Specht associés aux diagrammes de permutations. Nous montrons comment la structure de cristal permet d’étudier le produit d’une fonction de Schur avec une $k$-fonction de Schur. En conséquence, nous prouvons que la sous-classe des invariants de 3-points de Gromov–Witten d’une variété complète de drapeaux complets pour $\mathbb{C}^n$ énumère les éléments de poids maximaux pour ces opérateurs.

Defining Filtering Protective Suit Ideality using a Mathematical-Modeling Method

2019 ◽  
Vol 6 (6) ◽  
pp. 18-24 ◽  
Author(s):  
Dusan Rajic ◽  
Radovan Karkalic ◽  
Negovan Ivankovic ◽  
Pavel Otřísal
Keyword(s):  
Mathematical Modeling ◽  
Systems Approach ◽  
Reduction Process ◽  
Type A ◽  
System Engineering ◽  
Modeling Method ◽  
Expansion Process ◽  
Subsystem Level ◽  
The Ideal

Real systems approach the ideal by solving technical and physical contradictions. Optimization of system engineering (SE) is achieved when the problem is solved at the level of technical contradiction. When the problem is solved at the level of physical contradiction, the idealization of SE is achieved. Two possible ways of achieving ideality are described in this paper. The expansion process flows at the level of SE (i.e., idealization of another type), and the reduction process flows at the subsystem level (i.e., idealization of the first type). A procedure of mathematical modeling is presented for determining the level of ideality as a criterion for filtering protective suit (FPS) effectiveness, which can be used as a standard for determining the ideality of any SE.

scholarly journals On the K-Theory of the Coordinate Axes in the Plane

2007 ◽  
Vol 185 ◽  
pp. 93-109 ◽  
Author(s):  
Lars Hesselholt
Keyword(s):  
Intersection Point ◽  
Coordinate Ring ◽  
De Rham ◽  
K Theory ◽  
Witt Groups ◽  
The Ideal

AbstractLet k a regular noetherian p-algebra, let A = k[x, y]/(xy) be the coordinate ring of the coordinate axes in the affine k-plane, and let I = (x,y) be the ideal that defines the intersection point. We evaluate the relative K-groups Kq(A, I) completely in terms of the big de Rham-Witt groups of k. This generalizes a formula for K1(A, I) and K2(A, I) by Dennis and Krusemeyer.

TURBO-STRAIGHTENING FOR DECOMPOSITION INTO STANDARD BASES

1992 ◽  
Vol 02 (03) ◽  
pp. 275-290 ◽  
Author(s):  
CHRISTOPHE CARRE ◽  
ALAIN LASCOUX ◽  
BERNARD LECLERC
Keyword(s):  
Scalar Product ◽  
Young Tableaux ◽  
Symmetric Polynomials ◽  
Harmonic Polynomials ◽  
Technical Tool ◽  
Linear Basis ◽  
Plücker Relations ◽  
By Products ◽  
Main Technical Tool ◽  
The Ideal

Specht and Hodge have shown that the space generated by products of minors of a matrix admits a linear basis in bijection with Young tableaux. The decomposition of any element into this basis is called straightening and corresponds to the iterative use of Plücker relations. Thanks to a well-known isomorphism between the space of harmonic polynomials and the space of polynomials modulo the ideal generated by symmetric polynomials, we can now use as a main technical tool the canonical scalar product on this later space. This leads to a different, and possibly better, algorithm for straightening.

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