Howe duality
Web4 dec. 2007 · We study a dual pair of general linear Lie superalgebras in the sense of R. Howe. We give an explicit multiplicity-free decomposition of a symmetric and skew … Web9 mei 2024 · Howe duality is invoked to relate this result to the realization of R(3) as the algebra of the intermediate Casimir operators arising in …
Howe duality
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WebWe give a proof of the Howe duality conjecture in the theory of local theta correspondence for symplectic-orthogonal or unitary dual pairs in arbitrary residual characteristic. … Weba dual pair in the sense of Howe (cf. [H]). Following Howe, we have the isotypic decomposition Sd(C n O Cm) = M λ∈Pd min(n,m) V λ O mV λ (1) where Pd k is the set of partitions of d into at most k parts and nV λ (resp. mV λ) is the irreducible module of gl n (resp. gl m) with highest weight λ, and min(n,m) denotes the minimum of n and m.
Web1 dag geleden · Jae-Hoon Kwon, Sin-Myung Lee, Masato Okado. We introduce a category of -oscillator representations over the quantum affine superalgebras of type and construct a new family of its irreducible representations. Motivated by the theory of super duality, we show that these irreducible representations naturally interpolate the irreducible -oscillator ... Web9:30-10:30: Wee Teck Gan: On the Howe duality conjecture: Abstract: The theory of local theta correspondence was initiated by Howe in two influential papers written in the 1970’s. A fundamental conjecture in this subject is the Howe duality conjecture.
WebGurevich-Howe_Rank and duality in representation theory_2024.pdf (Verlagsversion), 805KB http://www-personal.umich.edu/~charchan/seminar/
The Howe duality conjecture for archimedean local fields was proved by Roger Howe. For -adic local fields with odd it was proved by Jean-Loup Waldspurger. Alberto Mínguez later gave a proof for dual pairs of general linear groups, that works for arbitrary residue characteristic. Meer weergeven In mathematics, the theta correspondence or Howe correspondence is a mathematical relation between representations of two groups of a reductive dual pair. The local theta correspondence relates … Meer weergeven • Reductive dual pair • Metaplectic group Meer weergeven Setup Let $${\displaystyle F}$$ be a local or a global field, not of characteristic $${\displaystyle 2}$$. Let $${\displaystyle W}$$ be a symplectic vector space over $${\displaystyle F}$$, and $${\displaystyle Sp(W)}$$ Meer weergeven • Gan, Wee Teck; Takeda, Shuichiro (2016), "A proof of the Howe duality conjecture", J. Amer. Math. Soc., 29 (2): 473–493, Meer weergeven
WebTHE HOWE DUALITY AND POLYNOMIAL SOLUTIONS FOR THE SYMPLECTIC DIRAC OPERATOR HENDRIK DE BIE, PETR SOMBERG, AND VLADIMIR SOUCEKˇ Abstract. We find the Fisher decomposition for the space of polynomials valued in the Segal-Shale-Weil representation. As a consequence, this allows to determine symplectic monogenics, … how did the religion of judaism beginWebdimensional representations of classical Lie algebras arising from the Howe’s reductive dual pairs (g,G), where g= sp 2n,so n and G= Oℓ,Sp2ℓ. 1. Introduction 1.1. Howe duality is a principle which gives a representation theoretic approach to the first fundamental theorem of the classical invariant theory [9, 10], and has played important ... how did the religion spreadWeb（1）Introduction to skew Howe duality： 摘要：The Reshetikhin-Turaev construction associated knot invariants to the data of a simple Lie algebra and a choice of irreducible representation. The Jones polynomial is the most famous example coming from the Lie algebra sl(2) and its two-dimensional representation. how did the refrigerator impact societyWeb2 sep. 2024 · We study general aspects of the reductive dual pair correspondence, also known as Howe duality. We make an explicit and systematic treatment, where we firs … how many students at centennial high schoolWeb29 jan. 2013 · resp ondances de Howe sur un c orps p-adique, Lecture Notes in Mathematics, vol. 1291, Springer-V erlag, 1987. [Pra93] Dip endra Prasad, Weil repr … how many students at capella universityWeb31 jan. 2024 · Howe duality and dichotomy for exceptional theta correspondences. We study three exceptional theta correspondences for p-adic groups, where one member of … how did the renaissance affect merchantsWeb8 aug. 2024 · It is hence not surprising to find, owing to Howe duality, that C (1234) = −2 K 1 and C (3456) = −2 K 2, namely that the intermediate Casimir operators corresponding … how many students at carroll high school