The Classical Groups

By H. Weyl. 1940

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

Accurate Force Field for Molybdenum by Machine Learning Large Materials Data (2017, background): “Atomic distance-based features such as Weyl matrices[26] and the histogram of pair distance distributions[27] cannot fulfill these requirements because they fail to provide a unique representation of the local environment[24].”
Representations of classical Lie groups and quantized free convolution (2013, unknown): “[W]) all irreducible representations of U(N) are parameterized by their highest weights, which are signatures — N–tuples of integers λ1 ≥ λ2 ≥ · · · ≥ λN .”
Operator bases, S-matrices, and their partition functions (2017, background): “1 by discussing the general irreducible representations (irreps) and characters of O(2r) [47].”
A New Approach to the Representation Theory of the Symmetric Groups. II (2005, background): “which is called the Schur–Weyl duality (see [ 1 ]).”
End-to-end Symmetry Preserving Inter-atomic Potential Energy Model for Finite and Extended Systems (2018, background): “For each object i , the symmetric matrix ) is an over-complete array of invariants with respect to translation and rotation [20, 22], i.e., it contains the complete information of the neighboring point pattern of atom i .”
Tensor diagrams and cluster algebras (2012, background): “ssions. We thank Bernard Leclerc and Gregg Musiker for their comments on the earlier version of the paper. Our main sources of inspiration outside cluster theory included the timeless texts by H.Weyl [53] andV.Popov–E. Vinberg [44]onthefoundations ofclassical invariant theory; the pioneering work by”
Simple current extensions beyond semi-simplicity (2015, background): “n O(n)- invariant good increasing ﬁltration in the sense of Li [Li2], and gr(H(n)O(n)) ∼= Ras differential graded commutative rings. Using Weyl’s ﬁrst fundamental theorem of invariant theory for O(n) [We], it is not difﬁcult to ﬁnd an (inﬁnite) strong generating set for gr(H(n)O(n)) consisting of an”
On the Hall algebra of an elliptic curve, I (2005, methodology): “The subalgebra generated by {�(0,n)} and the one generated by {T0,n} being equal, we see that W contains all Tr,n with |r| ≤ 1. Applying the first statement of the corollary, U ± ⊗ C ⊂ W, from which we deduce that W = UX ⊗ C.”
A singular minimizer of a smooth strongly convex functional in three dimensions (2000, methodology): “Now we use a classical procedure to decompose T into irreducible subspaces ( see [ We1 ]).”