scholarly journals Newton strata in the loop group of a reductive group

2013 ◽  
Vol 135 (2) ◽  
pp. 499-518 ◽  
Author(s):  
Eva Viehmann
Keyword(s):  
Reductive Group ◽  
Loop Group

scholarly journals Minimal Newton Strata in Iwahori Double Cosets

2019 ◽  
Author(s):  
Eva Viehmann
Keyword(s):  
Finite Subset ◽  
Minimal Element ◽  
Reductive Group ◽  
Double Coset ◽  
Loop Group ◽  
Conjugacy Classes ◽  
Regularity Assumption ◽  
Double Cosets

Abstract The set of Newton strata in a given Iwahori double coset in the loop group of a reductive group $G$ is indexed by a finite subset of the set $B(G)$ of Frobenius-conjugacy classes. For unramified $G$, we show that it has a unique minimal element and determine this element. Under a regularity assumption, we also compute the dimension of the corresponding Newton stratum. We derive corresponding results for affine Deligne–Lusztig varieties.

scholarly journals Generic Newton points and the Newton poset in Iwahori-double cosets

2020 ◽  
Vol 8 ◽  
Author(s):  
Elizabeth Milićević ◽  
Eva Viehmann
Keyword(s):  
Reductive Group ◽  
Loop Group ◽  
Index Set ◽  
Double Cosets ◽  
Large Classes ◽  
Bruhat Graph ◽  
Newton Stratification ◽  
Quantum Bruhat Graph

Abstract We consider the Newton stratification on Iwahori-double cosets in the loop group of a reductive group. We describe a group-theoretic condition on the generic Newton point, called cordiality, under which the Newton poset (that is, the index set for non-empty Newton strata) is saturated and Grothendieck’s conjecture on closures of the Newton strata holds. Finally, we give several large classes of Iwahori-double cosets for which this condition is satisfied by studying certain paths in the associated quantum Bruhat graph.

scholarly journals CONSTRUCTIVE NONCOMMMUTATIVE INVARIANT THEORY

2021 ◽  
Author(s):  
MÁTYÁS DOMOKOS ◽  
VESSELIN DRENSKY
Keyword(s):  
Lie Algebra ◽  
Associative Algebra ◽  
Invariant Theory ◽  
Reductive Group ◽  
Symmetric Tensor ◽  
Free Associative Algebra ◽  
Tensor Algebra ◽  
Enveloping Algebra ◽  
Finite Dimensional ◽  
Degree Bounds

AbstractThe problem of finding generators of the subalgebra of invariants under the action of a group of automorphisms of a finite-dimensional Lie algebra on its universal enveloping algebra is reduced to finding homogeneous generators of the same group acting on the symmetric tensor algebra of the Lie algebra. This process is applied to prove a constructive Hilbert–Nagata Theorem (including degree bounds) for the algebra of invariants in a Lie nilpotent relatively free associative algebra endowed with an action induced by a representation of a reductive group.

scholarly journals A decomposition formula for representations

1987 ◽  
Vol 107 ◽  
pp. 63-68 ◽  
Author(s):  
George Kempf
Keyword(s):  
Irreducible Representation ◽  
General Formula ◽  
Parabolic Subgroup ◽  
Characteristic Zero ◽  
Maximal Torus ◽  
Reductive Group ◽  
Irreducible Representations ◽  
Levi Subgroup ◽  
Know How ◽  
Decomposition Formula

Let H be the Levi subgroup of a parabolic subgroup of a split reductive group G. In characteristic zero, an irreducible representation V of G decomposes when restricted to H into a sum V = ⊕mαWα where the Wα’s are distinct irreducible representations of H. We will give a formula for the multiplicities mα. When H is the maximal torus, this formula is Weyl’s character formula. In theory one may deduce the general formula from Weyl’s result but I do not know how to do this.

scholarly journals Comparison of the clinical outcomes of skin bridge loop ileostomy and traditional loop ileostomy in patients with low rectal cancer

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Hui Ye ◽  
Shujuan Huang ◽  
Jie Yu ◽  
Qichang Zhou ◽  
Changlei Xi ◽  
...  
Keyword(s):  
Rectal Cancer ◽  
Low Anterior Resection ◽  
Clinical Evidence ◽  
Loop Ileostomy ◽  
Loop Group ◽  
Clinical Results ◽  
Low Rectal Cancer ◽  
Analog Scale ◽  
Traditional Group ◽  
Bridge Group

AbstractTo compare the clinical results of patients with low rectal cancer who underwent skin bridge loop ileostomy and traditional loop ileostomy, and provide clinical evidence for choosing a better ostomy method. We retrospectively collected data of 118 patients with rectal cancer who underwent low anterior resection and loop ileostomy. To investigate the patients characteristics, postoperative stoma-related complications and the frequency of exchanged ostomy bags. The differences of these indicators between the two groups of patients who underwent skin bridge loop ileostomy and traditional loop ileostomy were compared. The Visual Analog Scale (VAS) score of the skin bridge loop ileostomy group was lower than that of the traditional ileostomy loop group (P < 0.05). The skin bridge group had a lower Discoloration, Erosion, Tissue overgrowth (DET) score and incidence of mucocutaneous separation than the traditional group at the 1st and 2nd weeks after operation (P < 0.05). The average number of weekly exchanged ostomy bags was significantly less in the skin bridge group than in the traditional group within 4 weeks after surgery (P < 0.05). Our experience demonstrates that the skin bridge loop ileostomy may significantly reduce early postoperative stoma-related complications, the frequency of exchanged ostomy bags and patients’ medical costs after discharge.

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