Mudrās are specific gestures made using the hands for certain ritualistic or spiritual purposes. The jñāna-mudrā is one such mudrā, wherein the tarjanī (index finger) is joined to the anguṣṭha (thumb). This is specified in various tantra texts, for example:
aṅguṣṭha-tarjanībhyāṁ tu
jñāna-mudrā prakīrtitā
Translation: The jñāna-mudrā is formed by joining the index finger and the thumb. (Kaulāvalī-nirṇayaḥ, 7.44)
This mudrā is often displayed by great ācāryas of Vedantic traditions, especially by the revered Śrī Ādi Śaṅkarācārya.
At the same time however, we do not see any of the mūrtis of the six gosvāmīs displaying this mudrā. The deity of Śrīla Rūpa Gosvāmī and Śrīla Jīva Gosvāmī in the Rādhā-Dāmodara temple are also not in this mudrā. Why is it so that the mūrti of Śrīla Jīva Gosvāmī (the greatest Vedāntācārya of the Gauḍīya-vaiṣṇava-sampradāya) does not display the jñāna-mudrā?
The reason is that in the Bhakti-rasāmṛta-sindhuḥ, the jñāna-mudrā is associated specifically with those who are in śānta-rasa. The Bhakti-rasāmṛta-sindhuḥ (3.1.24 - 26) describes the anubhāvas (after-effects) of the individual who is experiencing śānta-rasa. One of the anubhāvas is:
jñāna-mudrā-pradarśanam — "Displaying the jñāna-mudrā". (Bhakti-rasāmṛta-sindhuḥ 3.1.24)
Śrīla Jīva Gosvāmī says in the Durgama-saṅgamanī commentary on this verse — jñāna-mudrā tarjany-aṅguṣṭhayor yutiḥ — "The jñāna-mudrā is displayed by joining the index finger and the thumb".
Śrīla Prabhupāda too specifies this in the Nectar of Devotion as follows: "When they speak, they join together the forefinger and thumb. (This is called the jñāna-mudrā position.) They are not against the atheists, nor are they particularly inclined to the devotees." (Nectar of Devotion, Chapter 35).
Clearly, the Gauḍīya-vaiṣṇava position is that this mudrā is displayed mainly by those who are experiencing śānta-rasa. However, none of the Gauḍīya-vaiṣṇavas are in śānta-rasa, because Śrī Caitanya Mahāprabhu has come to give ONLY FOUR rasas out of five — cāri bhāva-bhakti diyā (Caitanya-caritāmṛta, Ādi, 3.19).
The śānta-rasa is excluded in Mahāprabhu's flow of bhakti. The reason is that this particular rasa is mainly for the brahma-vādīs and paramātma-vādīs. The Caitanya-caritāmṛta clearly spells it out:
śāntera svabhāva—kṛṣṇe mamatā-gandha-hīna
paraṁ-brahma-paramātmā-jñāna pravīṇa
Translation: It is the nature of śānta-rasa that not even the smallest intimacy [towards Bhagavān] exists. Rather, knowledge of impersonal Brahman and localized Paramātmā is prominent. (Caitanya-caritāmṛta, Madhya, 19.218)
None of the Gauḍīya-vaiṣṇavas are interested in śānta-rasa. Gauḍīya-vaiṣṇavism begins with dāsya-rasa. Therefore, initiated names do not end with "śānta" (as in Hari Pārṣada "Śānta"). Instead, names end in "Dāsa" (Hari Pārṣada Dāsa).
This is the reason why we do not find any of the mūrtis of the six gosvāmīs in jñāna-mudrā. Even if some vaiṣṇava-sampradāyas have their respective ācārya-mūrtis in this mudrā, the Gauḍīya-vaiṣṇavas prefer other mudrās viz. āśīrvāda-mudrā (giving benedictions), chanting japa, namaskāra mudrā (folded hands) or writing some bhakti-śāstra. 
— Article and Translations by Hari Pārṣada "Dāsa". 13 June 2022.
