Titlebook: Representations of Lie Algebras and Partial Differential Equations; Xiaoping Xu Book 2017 Springer Nature Singapore Pte Ltd. 2017 Represen

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Root Systems we derive some basic properties of root systems. As finite symmetries of root systems, the Weyl groups are introduced and studied in detail. The classification and explicit constructions of root systems are presented. The automorphism groups of root systems are determined. As a preparation for late

最低點(diǎn)

sulcus

FLAGR

V洗浴

Nebulous

Representations of Odd Orthogonal Lie Algebrasure of the noncanonical oscillator representations obtained from the above bosonic representations by partially swapping differential operators and multiplication operators. Furthermore, we present a functor from the category of .-modules to the category of .-modules, which is related to .-dimension

防水

庇護(hù)

Representations of , and ,l module. Moreover, we present a one-parameter family of conformal oscillator representations of . derived from those of the simple Lie algebra of type . and determine their irreducibility. Furthermore, we use partial differential equations to find the explicit irreducible decomposition of the space

清真寺

Representations of ,on harmonic polynomials. Then we study the functor from the module category of . to the module category of .. Finally, we give a family of inhomogeneous oscillator representations of the simple Lie algebra of type . on a space of exponential-polynomial functions and prove that their irreducibility i

安裝

Representations of ,position of the polynomial algebra over the 56-dimensional basic irreducible module of the simple Lie algebra . into a sum of irreducible submodules. Then we study the functor from the module category of . to the module category of . developed. Moreover, we construct a family of irreducible inhomoge