Determinantal Ideals and the Canonical Commutation Relations: Classically or Quantized
نویسندگان
چکیده
We construct homomorphic images of $$su(n,n)^{{\mathbb {C}}}$$ in Weyl Algebras $${{\mathcal {H}}}_{2nr}$$ . More precisely, and using the Bernstein filtration , is mapped into degree 2 elements with negative non-compact root spaces being second order creation operators. Using Fock representation these homomorphisms give all unitary highest weight representations thus reconstructing Kashiwara–Vergne List for Segal–Shale–Weil representation. an idea from derivation their list, we a homomorphism $$u(r)^{{\mathbb whose image commutes vice versa. This gives multiplicities. The construction also easy proof that ideal $$(r+1)\times (r+1)$$ minors prime. Here, course, $$r\le n-1$$ fixed such r, space any irreducible annihilated by this ideal. As consequence, can be realized solutions to Maxwell type equations. actually go one step further determine exactly which our list there non-trivial between generalized Verma modules, thereby revealing, duality, covariant differential operators have null spaces. prove analogous results {U}}}_q(su(n,n)^{{\mathbb {C}}})$$ are replaced Hayashi–Weyl {H}}}{{\mathcal {W}}}_{2nr}$$ q-Fock space. Further, determinants q-determinants, {U}}}_q(u(r)^{{\mathbb constructed properties. For purpose Drinfeld Double used. mention difference: quantized spaces, while still 2, no longer given entirely
منابع مشابه
Exponential Representations of the Canonical Commutation Relations
A class of representations of the canonical commutation relations is investigated. These representations, which are called exponential representations, are given by explicit formulas. Exponential representations are thus comparable to tensor product representations in the sense that they provide the possibility of computing useful criteria concerning various properties. In particular, they are ...
متن کاملC-Multipliers, crossed product algebras, and canonical commutation relations
The notion of a multiplier of a group X is generalized to that of a C-multiplier by allowing it to have values in an arbitrary C-algebra A. On the other hand, the notion of the action of X in A is generalized to that of a projective action of X as linear transformations of the space of continuous functions with compact support in X and with values in A. It is shown that there exists a one-to-on...
متن کاملExact Discrete Analogs of Canonical Commutation and Uncertainty Relations
An exact discretization of the canonical commutation and corresponding uncertainty relations are suggested. We prove that the canonical commutation relations of discrete quantum mechanics, which is based on standard finite difference, holds for constant wave functions only. In this paper, we use the recently proposed exact discretization of derivatives, which is based on differences that are re...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Communications in Mathematical Physics
سال: 2022
ISSN: ['0010-3616', '1432-0916']
DOI: https://doi.org/10.1007/s00220-022-04524-5