Theta representation information

In mathematics, the theta representation is a particular representation of the Heisenberg group of quantum mechanics. It gains its name from the fact...

the theta representation, it acts on the space of holomorphic functions on the upper half-plane; it is so named for its connection with the theta functions...

In mathematics, theta functions are special functions of several complex variables. They show up in many topics, including Abelian varieties, moduli spaces...

={\begin{bmatrix}\cos \theta &-\sin \theta \\\sin \theta &\cos \theta \end{bmatrix}}{\begin{bmatrix}x\\y\end{bmatrix}}={\begin{bmatrix}x\cos \theta -y\sin \theta \\x\sin...

infinite-dimensional linear representation, the Weil representation. It was used by André Weil to give a representation-theoretic interpretation of theta functions, and...

{\begin{bmatrix}\theta &0\\0&-\theta \\\end{bmatrix}}=\theta {\begin{bmatrix}1&0\\0&0\\\end{bmatrix}}-\theta {\begin{bmatrix}0&0\\0&1\\\end{bmatrix}}=\theta (e_{1}-e_{2})...

data and its latent representation as Prior p θ ( z ) {\displaystyle p_{\theta }(z)} Likelihood p θ ( x | z ) {\displaystyle p_{\theta }(x|z)} Posterior...

(e^{i\theta })=e^{ik\theta },\quad k\in \mathbb {Z} .} We now let Σ {\displaystyle \Sigma } denote a finite-dimensional irreducible representation of K...

{\begin{bmatrix}\cos \theta +x^{2}(1-\cos \theta )&xy(1-\cos \theta )-z\sin \theta &y\sin \theta +xz(1-\cos \theta )\\z\sin \theta +xy(1-\cos \theta )&\cos \theta +y^{2}(1-\cos...

{\displaystyle Ae^{i(\omega t+\theta )}} is an analytic representation of A cos ⁡ ( ω t + θ ) . {\displaystyle A\cos(\omega t+\theta ).} Figure 2 depicts it...

Norwegian Resistance Theta representation of the Heisenberg group This disambiguation page lists articles associated with the title Theta group. If an internal...

spherical coordinate representation, ⟨ θ , φ | l m ⟩ = Y l m ( θ , φ ) {\displaystyle \langle \theta ,\varphi |lm\rangle =Y_{l}^{m}(\theta ,\varphi )} but...

mathematics, more specifically in group theory, the character of a group representation is a function on the group that associates to each group element the...

and existence of the induced representation. Let ( θ , W θ ) {\displaystyle (\theta ,W_{\theta })} be a linear representation of a subgroup H {\displaystyle...

{\displaystyle \rho _{n}^{*}(e^{i\theta })=[e^{-in\theta }]=\rho _{-n}(e^{i\theta }).} That is to say, the dual of the representation ρ n {\displaystyle \rho _{n}}...

ISBN 9783110885583 Lion, G.; Vergne, M. (1980), The Weil representation, Maslov index and theta series, Progress in Mathematics, vol. 6, Birkhäuser, ISBN 3-7643-3007-4...

Similar results are seen in the Segal–Bargmann space and in the theta representation of the Heisenberg group, where the creation and annihilation operators...

Q_{1}={\begin{bmatrix}1&0&0&0\\0&\cos(\theta )&\sin(\theta )&0\\0&-\sin(\theta )&\cos(\theta )&0\\0&0&0&1\end{bmatrix}}=\exp \left(\theta {\begin{bmatrix}0&0&0&0\\...

group Mumford-Tate group Mumford measure Mumford vanishing theorem Theta representation Manin–Mumford conjecture Horrocks–Mumford bundle Deligne–Mumford...

\theta )&=1&&=P_{0}(\cos \theta ),\\[4pt]T_{1}(\cos \theta )&=\cos \theta &&=P_{1}(\cos \theta ),\\[4pt]T_{2}(\cos \theta )&=\cos 2\theta &&={\tfrac...

{\displaystyle \theta } : θ ↦ z = e i θ = cos ⁡ θ + i sin ⁡ θ . {\displaystyle \theta \mapsto z=e^{i\theta }=\cos \theta +i\sin \theta .} This is the exponential...

Phi Theta Kappa Honor Society (ΦΘΚ or PTK) is an international honor society of students seeking associate degrees, bachelor's degrees, or other college...

t+\theta )}\ \ =\ e^{j|\omega |t}\cdot e^{j\theta },&{\text{if}}\ \omega >0,\\e^{-j(\omega t+\theta )}=\ e^{j|\omega |t}\cdot e^{-j\theta },&{\text{if}}\...

{\begin{aligned}R_{x}(\theta )&=e^{(-i\theta X/2)}=\cos(\theta /2)I-i\sin(\theta /2)X={\begin{bmatrix}\cos \theta /2&-i\sin \theta /2\\-i\sin \theta /2&\cos \theta...

\left({\frac {\theta }{2}}\right)-i\sigma _{3}\sin \left({\frac {\theta }{2}}\right)\right]\sigma _{3}\left[\cos \left({\frac {\theta }{2}}\right)+i\sigma...