相关论文: Determining whether certain affine Deligne-Lusztig…

In this paper, we study the emptiness/nonemptiness and the dimension formulas of affine Deligne-Lusztig varieties for $Sp_4(L)$. We mainly calculate the degree of class polynomials for the Iwahori-Hecke algebra of type $\widetilde{C}_2$.…

Diffeomorphism groups $G$ of manifolds $M$ on locally $\bf F$-convex spaces over non-Archimedean fields $\bf F$ are investigated. It is shown that their structure has many differences with the diffeomorphism groups of real and complex…

The affine Deligne-Lusztig variety $X_w(b)$ in the affine flag variety of a reductive group $\mathbb G$ depends on two parameters: the $\sigma$-conjugacy class $[b]$ and the element $w$ in the Iwahori-Weyl group $\tilde W$ of $\mathbb G$.…

Lusztig varieties are subvarieties in flag manifolds $G/B$ associated to an element $w$ in the Weyl group $W$ and an element $x$ in $G$, introduced in Lusztig's papers on character sheaves. We study the geometry of these varieties when $x$…

Let $(R,m)$ be a Noetherian local ring of characteristic $p>0$. We introduce and study $F$-full and $F$-anti-nilpotent singularities, both are defined in terms of the Frobenius actions on the local cohomology modules of $R$ supported at the…

Let g be a simple Lie algebra, with fixed Borel subalgebra b and with Weyl group W. Expanding on previous work of Fan and Stembridge in the simply laced case, this note aims to study the fully commutative elements of W, and their…

To any connected reductive group G over a non-archimedean local field F (of characteristic p > 0) and to any maximal torus T of G, we attach a family of extended affine Deligne-Lusztig varieties (and families of torsors over them) over the…

We study the nonnegative part B_{\ge 0} of the flag variety of a reductive algebraic group G, as defined by Lusztig. Using positivity properties of the canonical basis it is shown that B_{\ge 0} has an algebraic cell decomposition indexed…

We determine the structure of the W-group $\mathcal{G}_F$, the small Galois quotient of the absolute Galois group $G_F$ of the Pythagorean formally real field $F$ when the space of orderings $X_F$ has finite order. Based on Marshall's work…

We study the Newton stratification on SL_3(F), where F is a Laurent power series field. We provide a formula for the codimensions of the Newton strata inside each component of the affine Bruhat decomposition on SL_3(F). These calculations…

Let $G$ be a simple algebraic group defined over a finite field of good characteristic, with associated Frobenius endomorphism $F$. In this article we extend an observation of Lusztig, (which gives a numerical relationship between an…

We study the $J_b(F)$-action on the set of top-dimensional irreducible components of affine Deligne--Lusztig varieties in the affine Grassmannian. We show that the stabilizer of any such component is a parahoric subgroup of $J_b(F)$ of…

In this paper, we study the affine Deligne--Lusztig variety $X(\mu,b)_K$ and classify all quadruples $(\mathbf{G}, \mu, b, K)$ with $\dim X(\mu, b)_K=0$. This question was first asked by Rapoport in 2005, who also made an explicit…

For connected reductive groups together with a Frobenius root $F$, we show that the cohomology of the structure sheaf and respectively the canonical sheaf for compactified Deligne--Lusztig varieties associated to an element in the free…

Left invariant affine structures in a Lie group $G$ are in one-to-one correspondence with left-symmetric algebras over its Lie algebra $\mathfrak g=T_eG$ (``over'' means that the commutator $[x,y]=xy-yx$ coincides with the Lie bracket;…

Let $G$ be a connected reductive group over $\mathbb{C}$ with Weyl group $W$. Following a suggestion of Bezrukavnikov, we define a map from two-sided cells to conjugacy classes in $W$ using the geometry of the affine flag variety. This is…

We examine the set of $J_b(F)$-orbits in the set of irreducible components of affine Deligne-Lusztig varieties for a hyperspecial subgroup and minuscule coweight $\mu$. Our description implies in particular that its number of elements is…

In this paper we study the geometric structure of affine Deligne-Lusztig varieties for $GL_3$ and $b$ basic. We completely determine the irreducible components of the affine Deligne-Lusztig variety. In particular, we classify the cases…

We initiate the study of affine Deligne-Lusztig varieties with arbitrarily deep level structure for general reductive groups over local fields. We prove that for GLn and its inner forms, Lusztig's semi-infinite Deligne-Lusztig construction…

We determine the set of connected components of minuscule affine Deligne-Lusztig varieties for special maximal compact subgroups of unramified connected reductive groups. Partial results are also obtained for non-minuscule closed affine…