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Showing 1 to 20 of 34 for “"Grassmannian"”.
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The homotopy type of the matroid Grassmannian
… a homotopy equivalence between the matroid Grassmannian [parallel] MacP(k, n) [parallel] and the real Grassmannian G(k, n) of k-planes in [Real set]n. This is accomplished by finding a Schubert stratification of the former space and analyzing its relationship to the ordinary Schubert cell …
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Combinatorics related to the totally nonnegative Grassmannian
… appear in the study of nonnegative part of the Grassmannian. The classical theory of total positivity studies matrices such that all minors are nonnegative. Lustzig extended this theory to arbitrary reductive groups and flag varieties. Postnikov studied the nonnegative part of the Grassmannian, …
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Arrangement of minors in the positive Grassmannian
… Zelevinsky, are closely related to the positive Grassmannian and the associated cluster algebra. However, we also construct examples of arrangements of smallest minors which are not weakly separated using chain reactions of mutations of plabic graphs. In the second chapter, we investigate …
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Matrix Schubert varieties for the affine Grassmannian
… homology of the (special linear) affine Grassmannian by an analogous process. This requires finitizing an affine Schubert variety to produce a matrix affine Schubert variety. This involves a choice of ``window'', so one must then identify a class representative that is independent of this …
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Equivariant Quantum Cohomology of the Odd Symplectic Grassmannian
The odd symplectic Grassmannian IG := IG(k, 2n + 1) parametrizes k dimensional subspaces of C^2n+1 which are isotropic with respect to a general (necessarily degenerate) symplectic form. The odd symplectic group acts on IG with two orbits, and IG is itself a smooth Schubert variety in the …
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The Beilinson-Bernstein localization theorem for the affine Grassmannian
This thesis mainly deals with the study of the category of admissible modules for the affine Kac-Moody algebra at the critical level, and the study of its center.
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The eta invariant for manifolds with boundary and holomorphic maps into the the restricted Grassmannian
Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2001.
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Cotangent Schubert Calculus in Grassmannians
… (Kempf-Laksov) desingularization to the Grassmannian. We find that the Segre-MacPherson classes are stable under pullbacks of maps embedding a Grassmannian into a bigger Grassmannian. We also express these formulas using certain Demazure-Lusztig operators that have previously been used to …
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Equivariant quantum cohomology and the geometric Satake equivalence
… of this theory in the setting of the affine Grassmannian, a fundamental space in the geometric Langlands program. More precisely, we identify the equivariant quantum connection of certain symplectic resolutions of slices in the affine Grassmannian of a semisimple group G with a trigonometric …
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Combinatorial aspects of total positivity
… I study the totally non-negative part of the Grassmannian and prove an enumeration theorem for a natural cell decomposition of it. This result leads to a new q-analog of the Eulerian numbers, which interpolates between the binomial coefficients, the Eulerian numbers, and the Narayana numbers. …
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Presentations of Semigroup Algebras of Weighted Trees
… coordinate rings of weight varieties of the Grassmannian of two planes associated to the Pl\"ucker embedding, and as toric degenerations of rings of invariants of Cox-Nagata rings.
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Some results related to the quantum geometric Langlands program
… of spherical perverse sheaves on the affine Grassmannian of a reductive group G and the category of representations of its Langlands dual group. The category of spherical perverse sheaves sits naturally in an equivariant derived category, and this larger category was described in terms of the …
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Diagrams of affine permutations and their labellings
… an important role in the geometry of the affine Grassmannian. Furthermore, we define set-valued balanced labellings in which the labels are sets of positive integers, and we investigate the relations between set-valued balanced labellings and nilHecke words in the nilHecke algebra. A signed …
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Moduli Προβλήματα και Moduli Χώροι - Το πρόβλημα των αλγεβρικών καμπυλών
… βασικά παραδείγματα moduli χώρων, όπως τα Grassmannian και τα Hilbert schemes. Στη συνέχεια θα γίνει ανάλυση στις περιπτώσεις καμπυλών μικρού γένους (0 ή 1) και τέλος η κατασκευή του moduli χώρου Mg με εργαλεία της γεωμετρική θεωρίας αναλλοίωτων.
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Sigma Models with Repulsive Potentials
… image of the map to lie in a set homotopic to a Grassmannian.</p>
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Configuration Complexes and Tangential and Infinitesimal versions of Polylogarithmic Complexes
In this thesis we consider the Grassmannian complex of projective configurations in weight 2 and 3, and Cathelineau's infinitesimal polylogarithmic complexes as well as a tangential complex to the famous Bloch-Suslin complex (in weight 2) and to Goncharov's ``motivic`` complex (in weight 3), …
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Geometry Of Quivers
… projective variety can be considered as a quiver Grassmannian. The reasoning of the proof is demonstrated by example. We then prove the existence of a countable quiver containing every finite quiver as a subquiver. Following this we consider some properties of its category of representations. …
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Specht modules and Schubert varieties for general diagrams
… of the symmetric group, and the geometry of the Grassmannian are related to each other via Schur functions, Specht modules, and Schubert varieties, all of which are indexed by partitions and their Young diagrams. We will generalize these objects to allow for not just Young diagrams but arbitrary …
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Multivariable Interpolation Problems
… Krein-space geometry approach (also known as the Grassmannian Approach). To implement this approach J-versions of Beurling-Lax representers for shift-invariant subspaces are required. Here we obtain these J-Beurling-Lax theorems by the state-space method for both settings. We see that the …
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