Commentary, Res Rep Math Vol: 5 Issue: 12
Developments of Most High Weight Modules of Double Ringel-Hall Algebras By Means of Functions
Institute of Mathematics, University of Warsaw, Poland
Received Date: December 03, 2021; Accepted Date: December 17, 2021 ; Published Date: December 24, 2021
Citation: Rudnicki P (2021) Developments of Most High Weight Modules of Double Ringel-Hall Algebras By Means of Functions. Res Rep Math 5:12. 141.
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Keywords: symmetric group, trigonometric weight function
By using the set of involutions in the symmetric group, Anna Melnikov parametrized Borel orbits in the affine variety of squarezero n*n matrices. A similar combinatorics leads to the creation of a Bott-Samelson type orbit closure resolution. Fundamental classes, Chern-Schwartz-MacPherson classes, and motivic Chern classes in torus-equivariant theories can now be computed using cohomological and K-theoretic invariants of orbits. The formulas are in Demazure-Lusztig terminology. Information about cohomological and K-theoretic classes of the double Borel orbits in Hom (Ck , Cm) for k+m=n is included in the case of square-zero upper-triangular matrices. The relationship with double Schubert polynomials is recalled, and the Rimányi-Tarasov-Varchenko trigonometric weight function is interpreted similarly.
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A strong new viewpoint in the investigation of outright Galois groups has as of late risen up out of the investigation of Galois modules connected with classical defining spaces of specific Galois expansions. The repetitive pattern in these disintegrations is their shocking straightforwardness: practically all summands are free over some remainder ring. The sans non summands which seem are excellent in light of the fact that they are different in structure, but since they assume the key part in controlling math conditions that permit the leftover summands to be effortlessly depicted. Thusly, these outstanding summands are the lynchpin for a pack of new properties of outright Galois groups that have been gleaned from these amazing disintegrations.
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