scholarly journals Hurwitz spaces of coverings with two special fibers and monodromy group a Weyl group of typeBd

2012 ◽  
Vol 255 (1) ◽  
pp. 241-255 ◽  
Author(s):  
Francesca Vetro
Keyword(s):  
Weyl Group ◽  
Monodromy Group ◽  
Hurwitz Spaces ◽  
Special Fibers ◽  
Group A

scholarly journals On coverings with special points and monodromy group a Weyl group of type Bd

Filomat ◽  
2014 ◽  
Vol 28 (2) ◽  
pp. 275-284
Author(s):  
Francesca Vetroa
Keyword(s):  
Weyl Group ◽  
Monodromy Group ◽  
Hurwitz Spaces ◽  
Group A ◽  
Special Points

In this paper we study Hurwitz spaces parameterizing coverings with special points and with monodromy group a Weyl group of type Bd. We prove that such spaces are irreducible if k > 3d ? 3. Here, k denotes the number of local monodromies that are reflections relative to long roots.

scholarly journals Connected Components of H_(r,g)^A (G)

2018 ◽  
Vol 22 (2) ◽  
pp. 106
Author(s):  
Haval M. Mohammed Salih
Keyword(s):  
Computer Algebra ◽  
Computer Algebra System ◽  
Monodromy Group ◽  
Riemann Sphere ◽  
Primitive Group ◽  
Connected Components ◽  
Branch Points ◽  
Genus Zero ◽  
Hurwitz Spaces ◽  
Hurwitz Space

The Hurwitz space   is the space of genus g covers of the Riemann sphere  with  branch points and the monodromy group . In this paper, we enumerate the connected components of the Hurwitz spaces  for a finite primitive group of degree 7 and genus zero except . We achieve this with the aid of the computer algebra system GAP and the MAPCLASS package.

scholarly journals Ekedahl-Oort Strata for Good Reductions of Shimura Varieties of Hodge Type

2018 ◽  
Vol 70 (2) ◽  
pp. 451-480 ◽  
Author(s):  
Chao Zhang
Keyword(s):  
Weyl Group ◽  
Moduli Spaces ◽  
Level Structure ◽  
Reductive Group ◽  
Extension Property ◽  
Integral Model ◽  
Shimura Varieties ◽  
Shimura Variety ◽  
Canonical Models ◽  
Special Fibers

AbstractFor a Shimura variety of Hodge type with hyperspecial level structure at a prime p, Vasiu and Kisin constructed a smooth integral model (namely the integral canonical model) uniquely determined by a certain extension property. We define and study the Ekedahl-Oort stratifications on the special fibers of those integral canonical models when p > 2. This generalizes Ekedahl-Oort stratifications defined and studied by Oort on moduli spaces of principally polarized abelian varieties and those defined and studied by Moonen, Wedhorn, and Viehmann on good reductions of Shimura varieties of PEL type. We show that the Ekedahl-Oort strata are parameterized by certain elements w in the Weyl group of the reductive group in the Shimura datum. We prove that the stratum corresponding to w is smooth of dimension l(w) (i.e., the length of w) if it is non-empty. We also determine the closure of each stratum.

scholarly journals One-Dimensional Hurwitz Spaces, Modular Curves, and Real Forms of Belyi Meromorphic Functions

2008 ◽  
Vol 2008 ◽  
pp. 1-18 ◽  
Author(s):  
Antonio F. Costa ◽  
Milagros Izquierdo ◽  
Gonzalo Riera
Keyword(s):  
Dihedral Group ◽  
Meromorphic Functions ◽  
Monodromy Group ◽  
Elliptic Functions ◽  
Hurwitz Spaces ◽  
One Dimensional ◽  
Hurwitz Space ◽  
Upper Half Plane ◽  
Triangular Group ◽  
Real Forms

Hurwitz spaces are spaces of pairs(S,f)whereSis a Riemann surface andf:S→ℂ^a meromorphic function. In this work, we study1-dimensional Hurwitz spacesℋDpof meromorphicp-fold functions with four branched points, three of them fixed; the corresponding monodromy representation over each branched point is a product of(p−1)/2transpositions and the monodromy group is the dihedral groupDp. We prove that the completionℋDp¯of the Hurwitz spaceℋDpis uniformized by a non-nomal indexp+1subgroup of a triangular group with signature(0;[p,p,p]). We also establish the relation of the meromorphic covers with elliptic functions and show thatℋDpis a quotient of the upper half plane by the modular groupΓ(2)∩Γ0(p). Finally, we study the real forms of the Belyi projectionℋDp¯→ℂ^and show that there are two nonbicoformal equivalent such real forms which are topologically conjugated.

scholarly journals Limiting Directions for Random Walks in Classical Affine Weyl Groups

2021 ◽  
Author(s):  
Erik Aas ◽  
Arvind Ayyer ◽  
Svante Linusson ◽  
Samu Potka
Keyword(s):  
Random Walk ◽  
Weyl Group ◽  
Exclusion Process ◽  
Main Tool ◽  
Weyl Groups ◽  
Affine Weyl Groups ◽  
Type D ◽  
Simple Exclusion Process ◽  
Asymmetric Simple Exclusion ◽  
Group A

Abstract Let $W$ be a finite Weyl group and $\widetilde W$ the corresponding affine Weyl group. A random element of $\widetilde W$ can be obtained as a reduced random walk on the alcoves of $\widetilde W$. By a theorem of Lam (Ann. Prob. 2015), such a walk almost surely approaches one of $|W|$ many directions. We compute these directions when $W$ is $B_n$, $C_n$, and $D_n$ and the random walk is weighted by Kac and dual Kac labels. This settles Lam’s questions for types $B$ and $C$ in the affirmative and for type $D$ in the negative. The main tool is a combinatorial two row model for a totally asymmetric simple exclusion process (TASEP) called the $D^*$-TASEP, with four parameters. By specializing the parameters in different ways, we obtain TASEPs for each of the Weyl groups mentioned above. Computing certain correlations in these TASEPs gives the desired limiting directions.

scholarly journals Gröbner–Shirshov basis and reduced words for affine Weyl group Ãn

2014 ◽  
Vol 13 (06) ◽  
pp. 1450005
Author(s):  
Erol Yilmaz ◽  
Cenap Özel ◽  
Uğur Ustaoğlu
Keyword(s):  
Weyl Group ◽  
Affine Weyl Group ◽  
Group A ◽  
Partitions Of Integers ◽  
Reduced Words

Using Buchberger–Shirshov Algorithm, Composition–Diamond Lemma and partitions of integers we obtain the reduced Gröbner–Shirshov basis of Ãn and classify all reduced words of the affine Weyl group Ãn.

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