名著発掘 Hermann Weyl, The Classical Groups--Their Invariants and Representations

By 梅田亨. 2002

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Citations in the corpus

On the ideals of equivariant tree models (2007, background): “If X is a variety on which some group Γ acts, then S is called a Γ-subscheme if and only if ], and if S ⊆ X is a subscheme, then the image scheme of S is deﬁned as the scheme theoretic closure of f ( S ), i.e. the subscheme of Y deﬁned by the ideal ( f ♯ ) − 1 ( I ( S )).”
Cross Section and Panel Data Estimators for Nonseparable Models with Endogenous Regressors (2005, background): “Weyl (1939) page 39 provides a basis that is a generalization of the elementary symmetric functions for the case in which xik is a vector. must be compact).10 The jth elementary symmetric function is the sum of all products of j distinct variables xij ,with z ej i = P k1<k2...<kj xik1xik2 ...xikj ,…”
Representations of the Infinite Symmetric Group (2016, methodology): “Weyl computed the irreducible characters of the compact classical Lie groups U(N), SO(N), Sp(N) (see his famous book [133] and references therein).”
Functional maps (2012, background): “A famous example can be found in the field of Representation Theory (see for instance [Weyl 1946]).”
The design space of E(3)-equivariant atom-centred interatomic potentials (2022, unknown): “Nonetheless, they ﬁt into this framework by considering the equivalence of vectors and l = 1 spherical tensors.”
Differential Geometry and Lie Groups (2020, background): “339 7.10 Consequences of the Peter–Weyl Theorem . . . . . . . . . . . . . . . . . . . . . . . . 348 7.11 Gelfand Pairs, Spherical Functions, and Fourier Transform . . . 352 7.12 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .”
Gelfand-Tsetlin bases for classical Lie algebras (2002, methodology): “It is based on the Weyl realization of the representations of the classical groups in tensor spaces; see Weyl [136].”
Moment Tensor Potentials: A Class of Systematically Improvable Interatomic Potentials (2015, background): “We start with stating the first fundamental theorem for the orthogonal group O(d) [30].”
Vanishing theorems and character formulas for the Hilbert scheme of points in the plane (2001, background): “If the x variables x1, . . . , xn form an M -regular sequence, then (75) FM (z; q, t) = FM/(x)M [ Z 1−t ; q, t ] , and similarly with y and q in place of x and t. Proof.”