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Mathematics concept
In mathematics, the Satake isomorphism, introduced by Ichirō Satake (1963), identifies the Hecke algebra of a reductive group over a local field with
Satake_isomorphism
Topics referred to by the same term
Hiroshima, Japan Asteroid 8194 Satake Ichirō Satake (1927–2014), Japanese mathematician Satake isomorphism Satake diagram Misako Satake (佐竹 美佐子; born 1951), Japanese
Satake
Japanese mathematician
Satake isomorphism and Satake diagrams. He was considered an iconic figure in the theory of linear algebraic groups and symmetric spaces. Satake was born
Ichirō_Satake
Mathematical theory
{\displaystyle n=2,} the isomorphism s o 5 ≅ s p 2 {\displaystyle {\mathfrak {so}}_{5}\cong {\mathfrak {sp}}_{2}} corresponds to the isomorphisms of diagrams B 2
Compact_Lie_algebra
Finnish mathematician (born 1955)
commutative rings", which proved the geometric Satake equivalence, a geometric version of the Satake isomorphism. In 2013, Vilonen received a Humboldt Prize
Kari_Vilonen
form, which is unique up to isomorphism. It has maximal index among all real forms. The split form corresponds to the Satake diagram with no vertices blackened
Real_form_(Lie_theory)
Pictorial representation of symmetry
D_{5}} These isomorphisms correspond to isomorphism of simple and semisimple Lie algebras, which also correspond to certain isomorphisms of Lie group
Dynkin_diagram
A the set of isomorphism classes of pairs (E, φ), where E is a principal homogeneous space for G over Spec A[[t]] and φ is an isomorphism, defined over
Affine_Grassmannian
Branch of algebraic number theory concerned with abelian extensions
to be any finite abelian extension of F, this law gives a canonical isomorphism θ L / F : C F / N L / F ( C L ) → Gal ( L / F ) , {\displaystyle \theta
Class_field_theory
Monoidal category
conjecture; in other words, in bounding monodromy groups. The Geometric Satake equivalence establishes an equivalence between representations of the Langlands
Tannakian_formalism
Not-necessarily-associative commutative algebra satisfying (xy)(xx) = x(y(xx))
algebra up to isomorphism, it is often referred to as "the" exceptional Jordan algebra. Over the real numbers there are three isomorphism classes of simple
Jordan_algebra
complex rank. The Satake diagram has neither black vertices nor arrows. Every complex semisimple Lie algebra has a unique (up to isomorphism) split real Lie
Split_Lie_algebra
Unsolved problem in mathematics
as reciprocals of polynomials of p − s {\displaystyle p^{-s}} follows. Satake (1966) reformulated the Ramanujan–Petersson conjecture in terms of automorphic
Ramanujan–Petersson conjecture
Ramanujan–Petersson_conjecture
Variant of the notion of the center of a monoid, group, or ring to a category
object A {\displaystyle A} of C {\displaystyle {\mathcal {C}}} and an isomorphism u X : A ⊗ X → X ⊗ A {\displaystyle u_{X}:A\otimes X\rightarrow X\otimes
Center_(category_theory)
Generalized manifold
space. Definitions of orbifold have been given several times: by Ichirō Satake in the context of automorphic forms in the 1950s under the name V-manifold;
Orbifold
Type of Riemannian manifold
MR 1206066 Kurnosov, Nikon; Soldatenkov, Andrey; Verbitsky, Misha (2019), "Kuga-Satake construction and cohomology of hyperkähler manifolds", Advances in Mathematics
Hyperkähler_manifold
Concept in mathematics
reduces to classifying the simple Lie groups. These are classified by their Satake diagram; or one can just refer to the list of simple Lie groups (up to finite
Reductive_group
Space of complex matrices with positive definite imaginary part
{\mathcal {H}}_{g}} is not compact. A standard compactification is the Satake–Baily–Borel compactification A g ∗ {\displaystyle A_{g}^{*}} , obtained
Siegel_upper_half-space
Subgroup of the group of invertible n×n matrices
f: Gm → Gm defined by x ↦ xp induces an isomorphism of abstract groups k* → k*, but f is not an isomorphism of algebraic groups (because x1/p is not
Linear_algebraic_group
Function in harmonic analysis on groups
of zonal spherical functions and Hecke algebras was first developed by Satake and Ian G. Macdonald. The analogues of the Plancherel theorem and Fourier
Zonal_spherical_function
Direct sum of simple Lie algebras
{g}}{\overset {\sim }{\to }}\operatorname {Der} ({\mathfrak {g}})} is an isomorphism. (This is a special case of Whitehead's lemma.) As the adjoint representation
Semisimple_Lie_algebra
History of maths
Gelfand–Mark Naimark Gelfand–Naimark theorem (sometimes called Gelfand isomorphism theorem): The category Haus of locally compact Hausdorff spaces with
Timeline of category theory and related mathematics
Timeline_of_category_theory_and_related_mathematics
Manifold with inversion symmetry
described in detail in Koecher (1969) and Loos (1977) and summarized in Satake (1981). The development is in the reverse order from that using the structure
Hermitian_symmetric_space
travel, tourism, insurance
SATAKE ISOMORPHISM
SATAKE ISOMORPHISM
Boy/Male
Hindu
A musical note
Female
Italian
Italian form of Latin Natalia, NATALE means "birthday," or in Church Latin "Christmas day."
Male
Greek
(Σατάν) Greek form of Hebrew satan, SATAN means "adversary." In the bible, this is the name of the inveterate enemy of God. In the New Testament, Hebrew satan is translated once into Greek Diabolos, and once using the word epiboulos, meaning "plotter." This is also the Late Latin and Old English form of Hebrew satan.
Boy/Male
Hindu
One of the four spiritual son of Brahma
Male
Finnish
Pet form of Finnish Aarne, AAKE means "eagle."
Surname or Lastname
English and Scottish
English and Scottish : nickname for a wild or uncouth person, from Middle English, Old French salvage, sauvage ‘untamed’ (Late Latin salvaticus literally ‘man of the woods’, a derivative of Latin silva ‘wood’, influenced by Latin salvus ‘whole’, i.e. natural).Irish : generally of English origin (it was taken to County Down in the 12th century), this name has also sometimes been adopted as equivalent of Gaelic Ó Sabháin, the name of a small south Munster sept, which was earlier Anglicized as O’Savin (see Savin).Americanized form of Ashkenazic Jewish Savich.A Jacob Savage, born in Exeter, Devon, England, in 1604, is recorded in Essex, NJ, by the early 1630s. Edward Savage, of Huguenot descent, emigrated from Ireland to Massachusetts in 1696. His grandson and namesake, who was born in Princeton, MA, in 1761 gained fame as an artist for his portrait of George Washington (1789–90).
Girl/Female
Sikh
Virtuous brave
Surname or Lastname
English
English : nickname for someone thought to resemble a woodpecker in some way, Middle English spek(e) (a reduced form of Old French espeche(e), of Germanic origin).
Boy/Male
Hindu
(Brother of amavasu and vivasu)
Surname or Lastname
English
English : occupational name for someone who made and drove in stakes, or a topographic name for someone who lived near a boundary post for example, from a derivative of Middle English stake ‘post’, ‘stake’.
Girl/Female
Hindu
(Demoness (rakshasi) killed by Rama; mother of Mareecha)
Boy/Male
Hindu
Honor respect
Girl/Female
Hindu
Girl/Female
Hindu, Indian
Body Style
Surname or Lastname
English
English : variant of Speake.
Surname or Lastname
English
English : habitational name from any of the numerous places throughout England named from Middle English stoke. The exact sense in individual cases is not clear; it seems to have meant originally merely ‘place’, and to have been used mainly for an outlying hamlet or dependent settlement.
Boy/Male
Hindu
Another name for Ayodhya, City
Surname or Lastname
English
English : topographic name for someone who lived by a prominent post or stake, for example a boundary marker, from Middle English stake ‘post’, ‘stake’, or from the same word used as a nickname for a tall, thin person.
Boy/Male
Native American
Falcon.
Male
Finnish
Pet form of Finnish Sakari, SAKKE means "whom Jehovah remembered."
SATAKE ISOMORPHISM
SATAKE ISOMORPHISM
SATAKE ISOMORPHISM
SATAKE ISOMORPHISM
SATAKE ISOMORPHISM
SATAKE ISOMORPHISM
SATAKE ISOMORPHISM
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