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...

quantum physics Theta representation, a particular representation of the Heisenberg group of quantum mechanics Theta wave, in biology Theta*, a pathfinding...

{\displaystyle {\boldsymbol {\theta }}=\theta \mathbf {e} \,.} It is used for the exponential and logarithm maps involving this representation. Many rotation vectors...

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

\left({\begin{pmatrix}e^{i\theta }&0\\0&e^{-i\theta }\end{pmatrix}}\right)=e^{im\theta }+e^{i(m-2)\theta }+\cdots +e^{-i(m-2)\theta }+e^{-im\theta }.} This expression...

^{2}\theta &\sin ^{2}\theta &2\sin \theta \cos \theta \\\sin ^{2}\theta &\cos ^{2}\theta &2\sin \theta \cos \theta \\-\sin \theta \cos \theta &\sin \theta...

{\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})...

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

Hn. One representation of the Heisenberg group which is important in number theory and the theory of modular forms is the theta representation, so named...

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...

{\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}}...

(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...

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

as Lovász theta function and is commonly denoted by ϑ ( G ) {\displaystyle \vartheta (G)} , using a script form of the Greek letter theta to contrast...

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

mathematics, particularly q-analog theory, the Ramanujan theta function generalizes the form of the Jacobi theta functions, while capturing their general properties...

{\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...

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...

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

\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...

theta }&0\\0&e^{-i\theta }\end{pmatrix}}\right)={\frac {e^{i(m+1)\theta }-e^{-i(m+1)\theta }}{e^{i\theta }-e^{-i\theta }}}={\frac {\sin((m+1)\theta )}{\sin...

{\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...

θ } {\displaystyle \left\{1,e^{\pm i\theta }\right\}=\{1,\ \cos \theta +i\sin \theta ,\ \cos \theta -i\sin \theta \}} where i is the standard imaginary...

Nilpotent group Nilpotent Lie algebra Weil representation Theta representation Oscillator representation Weil, André. "Sur certains groupes d'opérateurs...

{\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...

field. The theta correspondence was introduced by Roger Howe in Howe (1979). Its name arose due to its origin in André Weil's representation theoretical...

Phi Theta Kappa (ΦΘΚ or PTK) is an honor society for students of associate degree-granting colleges. Its headquarters are in Jackson, Mississippi and...

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\\...